An improved pseudospectral approximation of coupled nonlinear partial differential equations
by A.K. Mittal; L.K. Balyan
International Journal of Computing Science and Mathematics (IJCSM), Vol. 15, No. 2, 2022

Abstract: In this paper, we propose a time-space Chebyshev pseudo-spectral method for the numerical solutions of coupled Burger's equation, Whitham-Broer Kaup shallow water model and coupled nonlinear reaction-diffusion equations. This technique is based on orthogonal Chebyshev polynomials which are discretised at Chebyshev-Gauss-Lobbato CGL points. A mapping is used to transform the non-homogeneous initial-boundary values to homogeneous initial-boundary values. By applying the proposed method in both time and space, the problem is reduced into a system of a nonlinear coupled algebraic equations which are solved using the Newton-Raphson method. Also present the error estimates in L₂− norm. The results obtained by the scheme are very accurate and effective. Presented numerical results confirm the spectral accuracy.

Online publication date: Thu, 07-Jul-2022

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