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Bhrawy, Ali H.; Assas, Laila M.; Alghamdi, Mohammed A.

An efficient spectral collocation algorithm for nonlinear Phi-four equations. (English) Zbl 1295.65100

Bound. Value Probl. 2013, Paper No. 87, 16 p. (2013).
Summary: A Jacobi-Gauss-Lobatto collocation method is developed to obtain spectral solutions for different versions of nonlinear time-dependent Phi-four equations subject to nonhomogeneous initial-boundary conditions. The node points are introduced as the roots of the orthogonal Jacobi polynomial with general parameters, \(\alpha\) and \(\beta\). The objective of this paper is thus to investigate the influence of the Jacobi spectral collocation method for solving the nonlinear Phi-four equations. Moreover, the results obtained with the different Jacobi polynomial parameters, \(\alpha\) and \(\beta\) are compared to examine the accuracy of most of these parameters. The accuracy and performance of the proposed method are assessed and evaluated through solving three nonlinear problems. Some numerical experiments are presented to show the convergence and the accuracy of the proposed algorithm.

Cited in 5 Documents

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35G31 Initial-boundary value problems for nonlinear higher-order PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

nonlinear Phi-four equations; nonlinear time-dependent equations; Jacobi collocation method; Jacobi-Gauss-Lobatto quadrature; implicit Runge-Kutta method; spectral collocation method; numerical experiment; convergence
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