Volume 37, Issue 5
A Linear Implicit L1-Legendre Galerkin Chebyshev Collocation Method for Generalized Time- and Space-Fractional Burgers Equation

Yubo Yang and Heping Ma

10.4208/jcm.1807-m2017-0197

J. Comp. Math., 37 (2019), pp. 629-644.

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  • Abstract

In this paper, a linear implicit L1-Legendre Galerkin Chebyshev collocation method for the generalized time- and space-fractional Burgers equation is developed. A linear implicit finite difference scheme based on the L1-algorithm for the Caputo fractional derivative is proposed for temporal discretization. And the Legendre Galerkin Chebyshev collocation method, based on the Legendre-Galerkin variational form, but the nonlinear term and the right-hand term are treated by Chebyshev-Gauss interpolation, is proposed for spatial discretization. Rigorous stability and convergence analysis are developed. Numerical examples are shown to demonstrate the accuracy, stability and effectiveness of the method.

  • History

Published online: 2019-03

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