Title: An improved pseudospectral approximation of coupled nonlinear partial differential equations

Authors: A.K. Mittal; L.K. Balyan

Addresses: Discipline of Mathematics, IIITDM Jabalpur, Madhya Pradesh, 482005, India ' Discipline of Mathematics, IIITDM Jabalpur, Madhya Pradesh, 482005, India

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.

Keywords: Coupled Burger's equation; Whitham-Broer Kaup shallow water model; coupled nonlinear reaction diffusion equations; pseudospectral method; Chebyshev-Gauss-Lobbato points.

DOI: 10.1504/IJCSM.2022.123999

International Journal of Computing Science and Mathematics, 2022 Vol.15 No.2, pp.155 - 167

Received: 26 Sep 2019
Accepted: 13 Mar 2020
Published online: 07 Jul 2022 *

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