Jacobi Collocation Methods for Solving Generalized Space-Fractional Burgers' Equations

doi:10.1007/s42967-019-00053-6

Abstract

Abstract: The aim of this paper is to obtain the numerical solutions of generalized space-fractional Burgers' equations with initial-boundary conditions by the Jacobi spectral collocation method using the shifted Jacobi-Gauss-Lobatto collocation points. By means of the simplifed Jacobi operational matrix, we produce the diferentiation matrix and transfer the space-fractional Burgers' equation into a system of ordinary diferential equations that can be solved by the fourth-order Runge-Kutta method. The numerical simulations indicate that the Jacobi spectral collocation method is highly accurate and fast convergent for the generalized space-fractional Burgers' equation.

Key words: Generalized space-fractional Burgers' equations, Jacobi spectral collocation methods, Diferentiation matrix, Shifted Jacobi-Gauss-Lobatto collocation points

CLC Number:

65M70
35R11

Qingqing Wu, Xiaoyan Zeng. Jacobi Collocation Methods for Solving Generalized Space-Fractional Burgers' Equations[J]. Communications on Applied Mathematics and Computation, 2020, 2(2): 305-318.

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