A Linear Implicit L1-Legendre Galerkin Chebyshev Collocation Method for Generalized Time- and Space-Fractional Burgers Equation
Year: 2019
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 629–644
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1807-m2017-0197
Journal of Computational Mathematics, Vol. 37 (2019), Iss. 5 : pp. 629–644
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Generalized fractional Burgers equation Stability and convergence analysis Legendre Galerkin Chebyshev collocation method Finite difference method.