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

Qingqing Wu; Xiaoyan Zeng

doi:10.1007/s42967-019-00053-6

Communications on Applied Mathematics and Computation ›› 2019, Vol. 2 ›› Issue (2) : 305-318. DOI: 10.1007/s42967-019-00053-6

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

Qingqing Wu¹ ,
Xiaoyan Zeng¹^,b

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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 simplified Jacobi operational matrix, we produce the differentiation matrix and transfer the space-fractional Burgers’ equation into a system of ordinary differential 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.

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Qingqing Wu, Xiaoyan Zeng. Jacobi Collocation Methods for Solving Generalized Space-Fractional Burgers’ Equations. Communications on Applied Mathematics and Computation, 2019, 2(2): 305‒318 https://doi.org/10.1007/s42967-019-00053-6