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.
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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.
Author Details
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Pointwise error estimate and stability analysis of fourth-order compact difference scheme for time-fractional Burgers’ equation
Zhang, Qifeng
Sun, Cuicui
Fang, Zhi-Wei
Sun, Hai-Wei
Applied Mathematics and Computation, Vol. 418 (2022), Iss. P.126824
https://doi.org/10.1016/j.amc.2021.126824 [Citations: 4]