scholarly journals Solving Two Dimensional Coupled Burger's Equations and Sine-Gordon Equation Using El-Zaki Transform-Variational Iteration Method

2021 ◽  
Vol 24 (2) ◽  
pp. 41-47
Author(s):  
Marwa H. Al-Tai ◽  
◽  
Ali Al-Fayadh ◽  
Keyword(s):  
Differential Equation ◽  
Iteration Method ◽  
Gordon Equation ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Partial Differential ◽  
Burger's Equations ◽  
Variation Iteration Method

In this paper, the combined form of the Elzaki transform and variation iteration method is implemented efficiently in finding the analytical and numerical solutions of the two-dimensional nonlinear coupled Burger's partial differential equations and sine-Gordon partial differential equation. The obtained solutions were compared to the exact solutions and other existing methods. Illustrative examples show the efficiency and the power of the used method.

scholarly journals Fractional variational iteration method for time-fractional non-linear functional partial differential equation having proportional delays

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 33-46 ◽  
Author(s):  
Durgun Dogan ◽  
Ali Konuralp
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Partial Differential ◽  
Data Set ◽  
Proportional Delays ◽  
Variational Iteration ◽  
Non Linear

In this paper, time-fractional non-linear partial differential equation with proportional delays are solved by fractional variational iteration method taking into account modified Riemann-Liouville fractional derivative. The numerical solutions which are calculated by using this method are better than those obtained by homotopy perturbation method and differential transform method with same data set and approximation order. On the other hand, to improve the solutions obtained by fractional variational iteration method, residual error function is used. With this additional process, the resulting approximate solutions are getting closer to the exact solutions. The results obtained by taking into account different values of variables in the domain are supported by compared tables and graphics in detail.

scholarly journals Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

scholarly journals Numerical solution of two dimensional time fractional-order biological population model

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 177-186 ◽  
Author(s):  
Amit Prakash ◽  
Manoj Kumar
Keyword(s):  
Approximate Solution ◽  
Fractional Order ◽  
Iteration Method ◽  
Population Model ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Spatial Diffusion ◽  
Two Dimensional ◽  
Degenerate Problem ◽  
Biological Population

AbstractIn this work, we provide an approximate solution of a parabolic fractional degenerate problem emerging in a spatial diffusion of biological population model using a fractional variational iteration method (FVIM). Four test illustrations are used to show the proficiency and accuracy of the projected scheme. Comparisons between exact solutions and numerical solutions are presented for different values of fractional orderα.

scholarly journals Perturbation-Iteration Method for First-Order Differential Equations and Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mehmet Şenol ◽  
İhsan Timuçin Dolapçı ◽  
Yiğit Aksoy ◽  
Mehmet Pakdemirli
Keyword(s):  
Differential Equation ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Single Equation ◽  
Iteration Algorithm ◽  
First Order ◽  
New Perturbation ◽  
First Time ◽  
Good Agreement

The previously developed new perturbation-iteration algorithm has been applied to differential equation systems for the first time. The iteration algorithm for systems is developed first. The algorithm is tested for a single equation, coupled two equations, and coupled three equations. Solutions are compared with those of variational iteration method and numerical solutions, and a good agreement is found. The method can be applied to differential equation systems with success.

Chebyshev Split-step Scheme for the Sine-Gordon Equation in 2+1 Dimensions

2013 ◽  
Vol 14 (1) ◽  
pp. 69-75
Author(s):  
Pablo Suarez ◽  
Stephen Johnson ◽  
Anjan Biswas
Keyword(s):  
Numerical Solution ◽  
Gordon Equation ◽  
Numerical Solutions ◽  
Time Integration ◽  
One Dimension ◽  
Fractional Step ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Spectral Convergence ◽  
Chebyshev Spectral Method

Abstract This article studies the numerical solution of the two-dimensional sine-Gordon equation (SGE) using a split-step Chebyshev Spectral Method. In our method we split the 2D SGE by considering one dimension at a time, first along x and then along y. In each fractional step we solve a 1D SGE. Time integration is handled by a finite difference scheme. The numerical solution is then compared with many of the known numerical solutions found throughout the literature. Our method is simple to implement and second order accurate in time and has spectral convergence. Our method is both fast and accurate.

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