Abstract
In this article, two new modified variational iteration algorithms are investigated for the numerical solution of coupled Burgers’ equations. These modifications are made with the help of auxiliary parameters to speed up the convergence rate of the series solutions. Three numerical test problems are given to judge the behavior of the modified algorithms, and error norms are used to evaluate the accuracy of the method. Numerical simulations are carried out for different values of parameters. The results are also compared with the existing methods in the literature.
Highlights
In recent years, coupled partial differential equations have been employed in various fields of engineering and applied sciences
Coupled Burgers’ equations are coupled partial differential equations (PDEs), and describe the approximation theory of flow through a shock wave traveling in a viscous fluid
The Chebyshev–Legendre pseudospectral method [7] has been utilized by Rashid et al for coupled viscous Burgers0 (VB) equations, where the leapfrog scheme and Chebyshev–Legendre Pseudo-Spectral method (CLPS) method were used for the time direction and space direction, respectively
Summary
In recent years, coupled partial differential equations have been employed in various fields of engineering and applied sciences. The following type of coupled Burger equations will be investigated:. Kya [4] used the decomposition method for the solution of a viscous coupled Burger equation, and obtained solutions in the form of a convergent power series. Arora [5] proposed a scheme known as the Lai cubic B-spline collocation scheme for the solution of coupled viscous Burger equations, where the authors used a crank Nicholson scheme and cubic B-spline functions for time integration and space integration, respectively. The Chebyshev–Legendre pseudospectral method [7] has been utilized by Rashid et al for coupled viscous Burgers0 (VB) equations, where the leapfrog scheme and Chebyshev–Legendre Pseudo-Spectral method (CLPS) method were used for the time direction and space direction, respectively. The organization of the rest of the paper is as follows; in Section 2, we elucidate the variational iteration algorithm-II, 3, the semi-numerical method is applied to three test problems, and a comparison is made with some other methods; lastly, some conclusions are drawn in the last Section 4
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