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Khater, A. H.; Temsah, R. S.; Callebaut, D. K.

Numerical solutions for some coupled nonlinear evolution equations by using spectral collocation method. (English) Zbl 1187.65114

Math. Comput. Modelling 48, No. 7-8, 1237-1253 (2008).
Summary: In this paper, we introduce a spectral collocation method based on Lagrange polynomials for spatial derivatives to obtain numerical solutions for some coupled nonlinear evolution equations. The problem is reduced to a system of ordinary differential equations that are solved by the fourth order Runge-Kutta method. Numerical results of coupled Korteweg-de Vries (KdV) equations, coupled modified KdV equations, coupled KdV system and Boussinesq system are obtained. The present results are in good agreement with the exact solutions. Moreover, the method can be applied to a wide class of coupled nonlinear evolution equations.

Cited in 7 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs

Keywords:

numerical solutions; Lagrange spectral collocation method; magnetohydrodynamics; plasma flow; coupled KdV equations; coupled modified KdV equations; coupled KdV system; Boussinesq system

Software:

PDESpecialSolutions
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Full Text: DOI Link

References:

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