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Quantitative Analysis of Long-term Dynamic Relationships between Crude Oil, gold, exchange rates, and stock prices: An Auto Regressive Distributive Lag Approach in Pakistan
Since crude oil is Pakistan's main source of imports, the current study empirically investigates the long-term dynamic relationships between changes in international price of crude oil and gold on macroeconomic indicators, particularly the exchange rate and stock market index. Therefore, international oil prices, Brent oil prices are used as a proxy which were obtained from Federal Reserve Economic Data (FRED) database, gold spot prices data were acquired from World Gold Council website, stock market index, KSE-100 index was used as a proxy and the data was collected from Investing.com website, and the data for exchange rate for Pakistani rupee against US Dollar (PKR/USD) was obtained from Investing.com. The sample period included in this study is from the year 2000 to 2021. The paper employs the Auto regressive Distributive Lag (ARDL) technique to analyze the dynamic relationships among the variables. Findings suggest ARDL has been useful in capturing the long-run relationship i.e., crude oil and gold international prices are significant variables and have impact on stock market and exchange rate.
An Algorithm Coded with R to Generate GN2 -designs in Circular Blocks
Minimal neighbor balanced designs are economical, therefore, these are preferred by the experimenters to minimize the bias due to neighbor effects. Minimal circular balanced neighbor designs cannot be constructed for almost every case of v even, where v is number of the treatments to be compared. For v even, the circular GN2-designs in which each treatment appears exactly once as neighbors with all other treatments except the one with which it appears twice, are considered the better alternate to the minimal balanced neighbor designs. In this article, an algorithm is developed to generate the circular GN2-designs for v even which can be converted directly into minimal circular balanced and strongly balanced neighbor designs. This algorithm is also coded with R.
Construction of Substitution Boxes Using Finite Fields
Substitution boxes (S-boxes) play a crucial role in modern cryptographic algorithms, providing non-linear transformations that enhance the security of data encryption. S-boxes are essential components of symmetric key ciphers, such as Advanced Encryption Standard (AES) and Data Encryption Standard (DES). Non-linearity is a fundamental property that resists linear attacks and enhances the cryptographic strength of S-boxes. Constructing secure and efficient S-boxes with high non-linearity is a critical challenge in cryptography. The problem of this research is to develop a systematic approach for constructingsubstitution boxes (S-boxes) using finite fields, with a particular focus on achieving optimal non-linearity to enhance the security of cryptographic algorithms.
Numerical analysis of flow rates, porous media, and Reynolds numbers affecting the combining and separating of Newtonian fluid flows
This study investigates the behavior of Newtonian fluids in pipes filled with and without porous media under combing and separating flow configurations. Numerical simulations are conducted to analyze the effects of changing flow rates, inertia, and porous media on flow patterns, vortex development, and pressure difference. The aim of this study is to examine the impact of inertia on flow behavior by analyzing the streamline patterns, vortex growth, and intensity at different Reynolds numbers, ranging from Re=1 to Re=5000.
Dynamic complexity of a discrete predator-prey model with prey refuge and herd behavior
This paper examines a discrete predator-prey model's complex dynamics. Using bifurcation and center manifold theory, we study period-doubling and Neimark-Sacker bifurcations at positive fixed points and their direction. Numerical simulations confirm the theoretical conclusions that the model's dynamics rely on Euler method step size. The model's behavior is also affected by the prey population's conservation rate. The model suggests that excessive conservation may reduce predator populations, causing food shortages. Thus, predator-prey dynamics management must account for prey conservation rate
Effects of Heat Transfer on Flow of MHD Maxwell Nanofluid on Stretching and Shrinking Surfaces.
In present article, there is studied heat, and the mass transfer characteristics of boundary layer flow of the Maxwell-nanofluid across stretching/shrinking surface along chemical reactions, transverse magnetic field and thermal radiation. Applying similarity transformation, the system of governing nonlinear PDEs are reduced into form of ODEs. The achieved equations are solved with help of bvp4c in Matlab computer software. The impacts of specified parameters include, suction parameter, Deborah number, magnetic parameter, thermophoresis parameter, chemical reaction parameter, Schmidt number, Brownian motion parameter, Prandlt number and thermal slip parameter are examined on velocity, temperature and nanoparticles concentration fields (profiles). Moreover, skin friction, Nusselt number and Sherwood number are achieved at numerous values of applied parameters which are demonstrated through graphs. Some of the key findings show that an increase in suction increases skin friction, Nusselt number and Shewood number along the variation of the stretching/shrinking parameter An increase in thermophoresis, magnetic and Brownian motion parameters increase the temperature fields of Maxwell nanofluid, while Deborah number, Prandtl number, suction parameter and thermal slip parameter decrease it.
Numerical Simulation of 2D Shallow water equation with constant external body force by using Finite difference method
In this paper the numerical modeling and simulation of 2D shallow water equations is discussed with the non-flat topography. The sets of these equations is solved by means of the Crank-Nicolson finite difference method with constant external body force and Darcy Weisbach equation is used for friction slope parameter. We have obtained the important results that, as soon as we start the time then Height evaluation function has the maximum amplitude wave length which is decreasing when the time increases. The numerical solution algorithm works well and enables to predict the water elevation and velocity at any instance and any location in the domain.
Average Error Based Adaptive Regularization Control For The Gradient Constancy Variational Stereo Model
The study of the stereo vision problems is most crucial and challenging task in image processing and computer vision. The Stereo Vision problems address the investigation of the correspondence between the two images of same scene (stereo pairs) captured from two different views. Generally, these problems are inverse and ill posed. To deal with such problems the energy-based regularization techniques are considered as an efficient and most successful approaches. The adaptive finite element method is used here as discretization method for the partial differential equation obtained from the optimization of the designed energy functional. Such type of the regularization generally depends on the smoothness parameters, and their suitable choice. The choice of the smoothing parameter in an adaptive way and specifically their choice as a scalar function over the whole computational domain is an interesting idea. In this work, a variational model based on the gradient constancy assumption is proposed, moreover a post optimization method (mesh refinement strategy) is designed which is based on a priori estimate called average absolute disparity error estimate. The post optimization is based on an adaptive intelligent algorithm which is efficient in identifying the less regular regions of the computed disparity image and reduces the value of the parameter to refine the grid. Consequently, the smoothness appears in the solution which is the main goal.
MHD flow and heat transfer of micropolar nanofluid on a linearly stretching/shrinking porous surface
In this paper, there is considered incompressible steady two-dimensional laminar MHD boundary layer flow, heat and mass transfer characteristics of micropolar nanofluid across a linearly stretching/shrinking porous surface. The effects of the magnetic, thermal slip, mass slip and heat source sink parameters are also considered. By applyingn appropriate similarity variables, the system of governing partial differential equations associated to micropolar nanofluid flow is transformed into a system of non - linear ordinary differential equations. The resulting equations are numerically solved in the Maple software by using shooting technique. The impact of the different applied parameters on skin friction, couple stress, Nusselt and the Sherwood numbers along the related profiles are determined for both stretching and shrinking cases of the surfaces. It was observed that with an increase in suction and magnetic parameters, the fluid velocity decreased. An increment in the thermal slip, the fluid temperature decreased and nanoparticles concentration decreases as the mass slip parameter is enhanced. An increase in concentration decreases but temperature increases. While, concentration and temperature both increase due to increase in thermophoresis parameter, and concentration also increases by increase in rate of chemical reaction. Thus, suction at the boundary and magnetic parameter acted as flow controlling parameter. It is believed that this type of investigation is very much helpful for the manufacturing of complex fluids and also for cleaning oil from surfaces.
The effect of uniform and exponential streams on Magnetohydrodynamic flows of viscous fluids.
In this research, we explore the equations of motion governing the behaviour of a finitely conducting incompressible fluid with variable viscosity, heat transfer, and the presence of a transverse magnetic field. By solving these equations, we obtain exact solutions that describe flows in which the vorticity distribution is varying indirect proportion to the stream function perturbed by both uniform and exponent streams. To obtain these exact solutions, we introduce a transformation variable that allows us ttransforming a non-linear system into a linear form the governing equations. From there, we are able to derive several exact solutions that provide insight into the behaviour of the fluid in these conditions.
Development of an Explicit Iterative Numerical Scheme Over the Modified Euler’s Method
The main theme of this research paper is to propose an explicit iterative numerical scheme over the modified Euler’s method (MEM) for solving initial value problems in ordinary differential equations. This iterative scheme has been proposed by changing the inner slope of the MEM by the mean of main slope of MEM and slope of explicit forward Euler’s method. The proposed iterative scheme has been tested for its performance by analyzing different numerical factors related to numerical algorithm and found it consistent, more accurate with the order of convergence 2 and it also shows greater stability region as compared to existing methods which are compared with proposed method.
Cubic Iterated Methods of Numerical Differential Method for Solving Non-Linear Physical Functions
In this research two iterated methods have been developed for solving non-linear equations, which arises in applied sciences and engineering. The proposed iterated methods are converged cubically, and it is derived from modified euler method and improved euler method with steffensen method. The cubic iterated methods of numerical differential method are work on physical application functions and compared with variant newton iterated method. The numerical outcome of proposed cubic iterated methods of numerical differential method is examined with C++/MATLAB. From the numerical results, it can be observed that the cubic iterated methods of numerical differential method are good for accuracy point of view, iteration perception and function evaluation as the assessment of variant newton iterated method for solving non-linear physical functions.
Simulation of 13 points Laplacian operator in cylindrical mesh system by using explicit ﬁnite difference technique
In nearest period of time a considerable and remarkable work have been done on the graphic design artificial intelligence, optimization, solving numerical approximation of ordinary as well as Partial differential equation by some differential operator, Discrete Laplacian operator is one of the most modern technique used for discretizatise the Ordinary differential equations (ODES) and Partial Differential equation (PDES). It is most simple technique, the researcher have taken great interest, as they may be able to find the novelty in their results specially in simulation of di-block co-polymer, solving the partial differential equation and also in finding light equation, wave equation in one as well as two dimension and etc. Discrete laplacian operator plays an essential role in the field of science and technology, shape interpolation, smoothing of the surface area, editing the meshes are the best usages of discrete laplacian operator In this study, a finite difference scheme is applied to develop the Laplacian operator using a cylindrical mesh system containing thirteen-point stencils. Laplacian operator has a significant role in the study of numerous mathematical and scientific phenomena. This employed in numerous significant computational and mathematical models, such as the Cell Dynamic Simulation system for the study of cutting-edge materials and image processing. The laplacian operator is necessary for being an isotropic discrete differential operator in a variety of models. When computing discrete isotropic results on curved surfaces, the curvilinear coordinate system may be a good option.
To Investigate Obstacle Conﬁguration Effect on Vortex Driven Combustion Instability
Combustion instability inside a chamber may lead to catastrophic failure. It is due to inappropriate combustion or ﬂow physics. Flow-driven instability is mostly governed by surface, corner, or obstacle vortex shedding. Inhibitors are placed inside a solid fuel combustion chamber to control the burning of the solid fuel grain. They burn slowly as compared to solid fuel and create protrusions inside the combustion chamber. These protrusions work as ﬂow obstacles. An obstacle vortex is shed from the inhibitor and produces pressure oscillations. The effects of inhibitor position on pressure oscillation inside a solid fuel combustion chamber is investigated in the present study. Large eddies must be resolved to compute vortex-driven ﬂow. Therefore, the Detached Eddy Simulation is applied to cylindrical combustion chambers having inhibitor and nozzle. Five different conﬁgurations are simulated. All parameters of different conﬁgurations are similar except inhibitor position. The inhibitor is moved upstream and downstream from the reference position to examine its effect on pressure oscillations. Pressure time histories at eight distinct places of the combustion chamber are recorded. Fast Fourier Transform (FFT) has been utilized to get pressure oscillation frequency and amplitude. It is interesting to reveal that the maximum amplitude of pressure oscillation occurs when the inhibitor to stagnation point distance is close to the combustion chamber diameter. It is up to 70% higher as compare to reference inhibitor position results. Computed results are also compared with available experimental data for validation purpose.
Study of second-order Hankel determinant for starlike functions with respect to symmetric points
The article aims to determine the sharp bounds of coeﬃcients, Fekete-Szegö, Zalcman inequalities for the family SS*_{tanh} of starlike function with respect to symmetric points linked with tan hyperbolic function. We also estimate determinant of | H_{2,2}(f) | is also obtained for the same class. Further, we study the logarithmic and inverse coeﬃcients for the same class.
Solution of Time-Fractional Third-Order Partial Differential Equations of One and Higher Dimensions
The purpose of this study is to develop the third order time fractional partial differential equations (PDEs) in one and higher dimensions, by taking Laplace Adomian decomposition method (LADM) and q-homotopy analysis transform method (q-HATM). To define fractional derivative, the Caputo operator is used for both fractional and integer orders. The solutions are obtained in the form of series. To understand the procedure of the suggested procedure, three numerical examples are taken. The graphs are plotted for the proposed solution at different values of fractional order ???? which is 0< ???? ≤ 1. Both proposed methods are implemented by using (LADM) and (q-HATM) showing that the proposed technique is found to be better and accurate instrument for solving linear and non-linear time fractional PDEs. The Novelty of the proposed study is that the provided solution for fractional order partial differential equations has never been attempted for third order, this means that the provided solution can solve the third order and could be generalized for the higher order also.
An Innovative Soft Rough Dual Hesitant Fuzzy Sets and Dual Hesitant Fuzzy Soft Rough Sets
This article seeks to demonstrate the novel properties of soft rough dual hesitant fuzzy sets (DHFSRSs) and dual hesitant fuzzy soft rough sets (SRDHFSs). The fundamental characteristics of DHFSRSs and SRDHFSs are thoroughly investigated. Additionally, we present a portrayal hypothesis for the DHFSRSs and SRDHFSs, which demonstrates that the level arrangements of the DHFSRSs and SRDHFSs can be used to characterize both the lower and upper DHFSRSs and SRDHFSs estimates in an identical manner.
The effect of oscillating streams on heat transfer in viscous magnetohydrodynamic MHD fluid flow
This study focuses on developing and proving exact solutions for equations of motion involving a fluid with finite conductivity, variable viscosities, and heat transfer in the presence of a transverse magnetic field. By utilizing a transformation variable, the governing equation is transformed into a assortment of simple ordinary differential equations, enabling accurate solutions to be achieved for the problem. The solutions demonstrate that the distribution of vorticity is proportional to the stream function, which is disturbed by oscillating (sine or cosine) or even and exponential streams. This study compares the profiles of steady fluid flow with changing viscosity and heat transfer travelling on a plane. The comparison is used to identify differences in the profiles of providing insight into the changes that occur in interesting factors. These findings have significant implications for understanding fluid dynamics in complex systems and may have important applications in fields such as engineering and physics.
The Hydrodynamics of Gravity-Driven Vessel Drainage of Third Order Fluid using Perturbation Method
This work clarifies the tank drainage problem of unsteady, incompressible and isothermal third-order fluid. The analytical solution is obtained from governing continuity and momentum equations for resulting non-linear PDE with no-slip conditions using the perturbation technique. The V(z) velocity profile, flow rate, depth H(t), time efflux, and time depth of the mass relation have been inspected on various parameters. The consequences of the depth H(t), the pipe having radius R, the density of the fluid ρ pipe of length L, dynamic viscosity µ, and small perturbation parameter ϵ on the velocity profile are beheld graphically. Comparison of Analytical result of the special case of third order fluid with existing literature when ϵ = 0 is given.
Improved Mid-Point Derivative based Closed Newton-Cotes Quadrature Rule
The main motivation for this work lies in the construction of new and efficient methods to improve the efficiency index of ‘Mid-Point Derivative Based Closed Newton-Cotes Quadrature Rules’. Proposed methods use the derivative values at the mid-points in each strip of integrations such as Mid-Point Derivative Based Closed Trapezoidal, Simpson One Third, Simpson Three eight and Bool’s Rule. The degree of precision and order of accuracy of proposed methods are higher than all the existing methods. Furthermore, error terms of the proposed methods are calculated by using the concept of precision. An extensive comparison of the proposed formulas, classical and mid-point quadrature rules for the number of function evaluation, error terms, coefficient of error terms and results obtained from some different problems are given. The comparisons illustrate that the new proposed Closed Newton-Cotes Rules are much superior to Classical Rules and Zhao and Li’s ‘Mid-Point Derivative Based Closed Newton-Cotes Quadrature’ schemes.
A Novel Two Point Optimal Derivative free Method for Numerical Solution of Nonlinear Algebraic, Transcendental Equations and Application Problems using Weight Function
It’s a big challenge for researchers to locate the root of nonlinear equations with minimum cost, lot of methods are already exist in literature to find root but their cost are very high In this regard we introduce a two-step fourth order method by using weight function. And proposed method is optimal and derivative free for solution of nonlinear algebraic and transcendental and application problems. MATLAB, Mathematica and Maple software are used to solve the convergence and numerical problems of proposed and their counterpart methods.
A new three step derivative free method using weight function for numerical solution of non-linear equations arises in application problems
Abstract In this paper a three-step numerical method, using weight function, has been derived for ﬁnding the root of non-linear equations. The proposed method possesses the accuracy of order eight with four functional evaluations. The eﬃciency index of the derived scheme is 1.682. Numerical examples, application problems are used to demonstrate the performance of the presented schemes and compare them to other available methods in the literature of the same order. Matlab, Mathematica 2021 & Maple 2021 software were used for numerical results.
Analysis of Two-Level Complex Shifted Laplace Preconditioner and Deflation-Based Preconditioner for Helmholtz Equation
A Long time deflation preconditioner is used to speed up the convergence of the Krylov subspace method. The discretization of Helmholtz equation with Dirichlet boundary condition by finite difference method obtained any linear system. Resolving a large wavenumber requires a larger number of Grid points, i.e. large linear systems. Thus due to the large linear system, many (sparse) direct methods have taken more memory, So we have used the (iterative technique) Krylov subspace method. One of the problems of the Krylov subspace method is the required preconditioner for better convergence. We use (CSLP) as a preconditioner and drive eigenvalues of (CSLP). However, with increasing wavenumber CSLP shows slow convergence behavior. Then we use another projection-type preconditioner as a deflation preconditioner. A rigorous Fourier analysis (RFA) is a separate research idea to examine the con- vergence of the iterative method included in this article. We analyze the deflation preconditioner with a complex shifted Laplace preconditioner (CSLP) which exhibition spectral behavior of the preconditioner, which is favorable to the Krylov method.
The melting behavior of Paraffin RT-50 in a finned cylindrical surface
The energy provision is one of the main concerns of modern technological processes and thermal management systems. Through latent heat energy, the storage of thermal energy using phase-change materials is examined in this paper. Paraffin Rubitherm 50 is filled in the cylinder. The base of the cylinder is heated and the vertical surface is made adiabatic. The melting procedure for two cases namely the plane surface and finned surface of the cylinder are considered. The melt fractions are observed and photographed for fixed intervals of time from solid state to total melt state. Initially, the melting of specified PCM was slow and then it became faster when convection heat transfer is accompanied with the conduction. The melting of PCM is geared with fin presence.
Effect of Slip Condition on Unsteady Tank Drainage Flow of third Order Fluid
Unsteady, isothermal, and incompressible third-order fluid is considered in the tank, cylindrical coordinates are taken into account and the flow of the fluid is considered in the z-direction. The behavior of viscoelastic fluid is analyzed with slip conditions. Velocity profile, flow rate, and mathematical relation between time depth of mass and time efflux, etc. are calculated with the perturbation method. Perturbation is a suitable technique for nonlinear partial differential equations because it converts them into the linear form which is easy to solve. Different physical flow parameters are inspected graphically. A comparison of slip and no-slip is presented also Newtonian and third-order fluids are compared too.
Exact solution on the impact of slip condition for unsteady tank drainage ﬂow of Ellis ﬂuid
In this paper, we look into the effect of slip condition on isothermal and incompressible Ellis fluid of an unsteady tank drainage flow. The non-linear PDE (partial differential equation) is solved exactly by applying the governing continuity and momentum equations, subject to the proper boundary condition, using the separation of variables approach. Unique situations this model put out by Ellis fluid is used to develop concepts like Newtonian, Power law model, and Bingham Plastic model solution. On setting the slip parameterexact solution for Ellis fluid flow is retrivred as well as Newtonian solution is bring back, which was done through Bernoulli's equation. Expressions for velocity field, pipe shear stress, volume flux, velocity average, depth of fluid in the tank at different times and also the relationship between length of the time be different with depth of the tank and the length of time required to complete the drainage is determined. Graphical representation is given of the effects of various development factors on the velocity field Vz and fluid depth H(t). The tank can empty faster for Ellis fluid compared to its special situations, according to the analogy of Ellis, Power law, Newtonian, and Binghan plastic fluids for the relation of depth with respect to time.
Optimum solutions of partial diﬀerential equation with initial condition using optimization techniques
This paper proposes a new minimization technique for the solutions of partial diﬀerential equation with initial conditions. The proposed procedure is used to minimize the obtained solutions through any numerical technique. For the minimization process, Non-linear Nelder-Mead Simplex algorithm and genetic algorithm are used as optimization techniques. The designed partial diﬀerential equation has been calculated as an error function for the minimization process. Both Non-linear Nelder-Mead Simplex and genetic algorithm guarantees the minimization of nonlinear partial diﬀerential equation with initial conditions. The resultant technique has a global validity for the solutions minimization of partial diﬀerential equations. Non-linear Nelder-Mead simplex showed better performance than genetic algorithm when tested on numerical instances.
Effect of the Arbitrary Coefficients on the convergence of numerical solution of General Second Order Linear Homogeneous Partial Differential Equation
In this study the eﬀect of the coecients on the convergence of numerical solution of general second order linear homogeneous partial diﬀerential equation has been investigated. The main objective was to determine the sensitivity of the coecients of the PDE in relation to the domain and mesh size. The nite diﬀerence method was used to discretize the PDE and numerical solution was obtained by implementing the algorithm on MATLAB. The outcomes of the research have provided interesting facts about the stable values of the coecients. From the results it is found that the arbitrary coecients d and e are more sensitive as compared to a, b, c and f. The outcomes of this research study are expected to provide the ways to predict and control the numerical solution convergence behavior obtained by the general second order PDE based on the variable coecients of the PDE.
Power Hamy Mean Operators for managing Cubic Linguistic Spherical Fuzzy Sets and their Applications
In modern social administrative economic activities, we are facing a considerable amount of multi-attribute group decision making problems. The methods and theory related to this method are very useful in the field of particular disciplines as well as in operational research, and a lot of achievements have been described. Obviously the real world is full of uncertainties and classical set theory cannot be used to describe different phenomena such as beauty, intelligence, height (tallness) and age etc. This thing leads mathematicians to develop the notion of fuzzy sets. Later Zadeh introduced the concept of membership and non-membership degree. Definitely human opinion about a phenomenon may be unidirectional or multi-directional, that’s why Atanossov proposed the concept of another advance type of fuzzy sets, which is known as intuitionistic fuzzy sets. His concept is based on a degree of membership and degree of non-membership with a exquisite that their sum must not exceed 1. In our work we introduced cubic linguistic spherical fuzzy sets. Then, we proposed the fundamental operation law for CLSFVs and a series of their average operators (AOs), such as the (cubic linguistic spherical fuzzy power average), (cubic linguistic spherical fuzzy power weighted average), (cubic linguistic spherical fuzzy power hamy mean) and (cubic linguistic spherical fuzzy power weighted hamy mean) operators, was developed by combining the power average and hamy mean operators in cubic linguistic spherical fuzzy environment. Also we described some specific desirable properties of all these operators. In addition, we suggested a new MAGDM method.
Assessment of the COVID-19 Pandemic's Impact on Gasoline Prices in Pakistan
Abstract The COVID-19 virus is a pandemic that, from the outset, alters its appearance and symptoms. It has aggressively spread around the world. The COVID-19-induced fear and uncertainty are disrupting the global economy and exacerbating ﬁnancial market volatility. The most impacted countries were the United States, the United Kingdom, India, and Pakistan. The continuing COVID-19 situation is both a public health and economic concern on a worldwide. This research aims at how the spread of the COVID-19 has affected the cost of gasoline, diesel, and liqueﬁed petroleum gas (LPG). Every week, statistics on COVID-19 instances and pricing are collected. The data was analyzed using the ARDL model and the Bound test to determine the short and long-term association between COVID-19 and prices. The Autoregressive distributive lag model ﬁndings reveal that conﬁrmed and mortality cases impact fuel, diesel, and LPG prices.
Analysis of Entropy-dependent solitons in ETG-driven magneto plasma by Variational Iteration Method
Nowadays, the discovery of the link between entropy and plasma density and temperature opens up new avenues for mathematicians and researchers to examine alternative plasma models in terms of entropy. The linear dispersion relation and KdV equation are created after the entropy drift is taken into account in the ETG mode. In addition, the Variational Iteration Technique (VIM) is used to determine the problem’s analytical solutions. Involving the Langrange multiplier also helps to accelerate computation and lower its cost. Then, it is shown that in ETG mode, entropy impacts both the breadth and amplitude of rarefactive solitons, as well as the impact of inhomogeneity drift and the magnetic ﬁeld on the conﬁguration of solitons. In this instance, however, only the rarefactive solitons are present. Since introducing entropy to the system might alter the previous plasma ﬁndings, this study is new. Finally, the current approach will be applied to the entropy-based in magnetically restrained plasmas, solitary waves can be observed. The graphical ﬁndings are also provided using Maple-18.
Using Crank-Nicolson’s scheme to discretize the Laplacian in a polar gird system with symmetric and asymmetric lines
Numerous techniques exist for solving and describing the Partial differential equation’s mathematical and computational model. The Laplacian operator is one of the most effective techniques for solving linear and nonlinear partial differential equations. It is quick, and researchers use it frequently because of its modern technique and high accuracy in results. The Crank-Nicolson (CN) scheme in the Cartesian coordinate system has been discussed in this research work. Using this method, a numerical approximation scheme in Cartesian coordinate system has been discretized on a 5 point stencil, extendable to nine points. The Tailor Series was used to discretize this scheme on 5-point stencils, which will be used in FORTRAN code for numerical approximation and can be visualized in OPEDX software. The Nicolson scheme is a ﬁnite difference scheme used to solve partial differential equations such as heat, wave, and diffusion equations in both 1-D and 2-D. Because of his extendable stencil, it will create accuracy and stability in the novel results of the scheme. These extendable stencils will reduce the error of the scheme and will assist researchers in ﬁnding novel results by solving ODES and PDES using the CN method.
Analytical Solution of Transient Flow of Fractional Oldroyd-B Fluid between Oscillating Cylinders
This paper investigates the fractional Oldroyd-B ﬂuid ﬂow across two interminable coaxial cylinders, where the ﬂuid’s motion is generated by the oscillatory movement of cylinders and the oscillating pressure gradient. The proﬁle of velocity and shear stress of the ﬂow is derived with the assistance of Caputo fractional derivative utilizing an analytical technique, ﬁnite Hankel transform and Laplace transforms. The semi-analytical solution is then displayed as generalized functions of G and R satisfying fundamental constitutive equations and all initial and boundary conditions. To validate the results, some limitations have been imposed on the determined equations and the results have been contrasted against previous results. Moreover, the inﬂuence of various parameters on the ﬂow of fractionalized Oldroyd-B ﬂuid is investigated and depicted graphically.
Delta Perturbation Method for Couette-Poiseuille flows in Third grade fluids
This work uses the Delta Perturbation Method (DPM) to theoretically evaluate the steady plane Couette-Poiseuille flowbetween two parallel plates for third-grade fluid.That'sa kind of perturbation approach and was deliveredwith the aid of Bender and his colleagues in the 1980s. Utilizing DPM, analytical solutions have been found from the governing continuity and momentum equations subject to the necessary boundary conditions. In this proposed model, the Newtonian solution is obtained through the substitution. It is possible to measure the velocity field, temperature distribution, volumetric flow rate, and average velocity of the fluid flow. We derived that the third-grade fluid's velocity will change in response to an increasing material constant from the visual and table representations of the impacts of different parameters on the velocity and temperature profiles.The suggested model additionally mentions temperature distribution losses with increases in thermal conductivity and rises as a result of increases of dynamic viscosity , constant parameters and and material constant. Here we have also find out that temperature distribution and velocity profile enhance with higher magnitude of pressure gradient
Unsteady Flow of an MHD Tangent Hyperbolic Nanoﬂuid Over a Stretching Sheet
Abstract The recent article addresses the unsteady ﬂow of MHD incompressible tangent hyperbolic ﬂuid with Nanoﬂuid particles in the direction of a stretching surface. Nano-ﬂuid is related to thermo-phoretic and Brownian movement. With proper help through the transformation procedure, the set of non-linear (PDEs) is re-framed into (ODEs). The initiate expressions of momentum, temperature ﬁeld, and nano-particle concentration are composed into groups of nonlinear equations. That consequential terminology is computed shooting system. The impact of fundamental parameters on the ﬂow ﬁeld, thermal circulation, and meditation is described. Moreover, the ﬂow ﬁeld behavior due to the Wall friction, local Nusselt, and Sherwood numbers are examined. This study is signiﬁcant as this transformation determined the shooting technique’s numerical result and ensured the physical parameters’ behavior graphically. The results show that the velocity ﬁeld diminishes by escalating the Weissenberg (We) ﬁgure and power-law index (n), while thermal and concentration ﬁelds remain to detect elevating at similar parameters. Furthermore, the computed result is compared with existing literature and gets accuracy.
Marketing Competence of Cellular Networks in Mardan, Pakistan
Maintaining and expanding a reliable customer bank is an intimidating target for cellular phone service providers. Marketing drives are arranged to gain valuable insight into consumer’s preferences and service packages accordingly by network providers from time to time. The study aim is to check the demand and service quality of the Zong network in Mardan City in the presence of its competitors. A sample of 400 respondents was selected at random from Mardan City and surrounding areas, having 61% males and 39% female respondents. The questionnaire method was applied to collect purposeful data to get the conclusions. The ﬁndings indicated that Zong (37.2%) is being used by the majority of the respondents followed by Ufone (20.8%) and Telenor (18.4%). Being its good quality services, 59.2% of the respondents are in favor to use the Zong network, 57.2% of consumers are using Zong just because of its low tariff, and 46.6% of respondents are unsure to switch off the Zong connection in the next coming 5 or more months.
Image Driven Isotropic Diffusivity and Complementary Regularization Approach for Image Denoising Problem
We present the idea of image driven isotropic diffusivity along with complementary regularization for image denoising problem. The method is based on the optimization of a quadratic function in L2 norm. The minimization of the energy functional leads to the Partial Differential equation (PDE)-based problem. We are looking for a steady state solution of equivalent time dependent problem. We discretize the problem with standard ﬁnite differences. The steady-state numerical solution of the time dependent problem leads to the iterative procedure, which allow to compute a regularized version of the solution as a denoised image. We have applied our designed model on synthetic as well as real images. The numerous experiments have been conducted to analyse the performance of the method for the different choices of scaling parameters. From the quality of the obtained results and comparative study it is observed that the proposed model performs well as compared to well existing methods.
Algebra Based Encryption and Decryption Algorithms
In this study an encryption/decryption algorithm is proposed and developed. The developed algorithm is based on the idea that any given plain text can be encrypted like a block cipher with a combination of three encryption keys k1, K2, ...KN that use any value between N = 1, 2, 3, n, . Then the cipher values can be used to make the blocks of alphabets containing only A, B, C, D, E, F, G, H, I, J, each block is separated by a space. The steps of algorithm could also be reversible for decryption of the cipher text. A MATLAB code is written to implement the algorithm and tested different input messages.Secret message consists of website link and bank account details. The specialty of the algorithm is that it can be ﬂexibly used to encrypt and decrypt the secret messages containing not only English alphabets but also those messages containing the numbers, punctuations, elementary mathematics operations and the special characters. The performance of the algorithm is evaluated in terms of computational time, memory usage. From the analysis it is found that the proposed algorithm is faster in terms of execution time as compared to the modern algorithm which makes the algorithm computationally secure. The proposed research particularly contributes as the addition of knowledge in the ﬁeld of cryptography and generally to the information security; consequently can be beneﬁcial to the society. 3
3D Finite Difference Formulation and Simulation of EHD Ion-Drag Model
This paper presents the simulation of electrohydrodynamically driven micropump obtained by using 3D ﬁnite difference method. EHD governing equations are discretized and then explicitly deﬁned for output parameters. A 3D prototype of ion-drag micropump with symmetric electrodes is modeled and simulated for the velocity, the pressure, electric potential and electric ﬁeld. The objective of this study was to evaluate the results obtained by ﬁnite difference method (FDM) with the results obtained by a ﬁnite element method (FEM) based simulation package COMSOL Multiphysics. The comparison reveals that the numerical simulation results obtained by both the methods are appreciably close to each other. The simulation results are also compared with the existing ex- perimental data and it was found that there are not high discrepancies between simulation and experimental results. The paper concludes that in case of regular geometries of ion-drag micropump the FDM is easy to implement and provides more control on different parameters involved in the simulation as compared to built-in ﬁnite element method based package.
Exact solution of some non‎linear PDE‎$ ‎‎{s} $ ‎with‎ conformable fractional derivative
‎In this article‎, the reduced differential transform method is improved to solve some nonlinear conformable time fractional partial differential equations. The solutions obtained by the purposed methd to solve the Korteweg-de Vries equation, k(m,n) for ‎ m=n=2, and Wu-Zhang (2+1)-dimensional dispersive long wave equation, show that the method is very effective.