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

Yubo Yang & Heping Ma

DOI: 10.4208/jcm.1807-m2017-0197

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

Published online: 2019-03

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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.

  • Keywords

Generalized fractional Burgers equation, Stability and convergence analysis, Legendre Galerkin Chebyshev collocation method, Finite difference method.

  • AMS Subject Headings

65M70, 65M12, 65M15, 26A33, 35R11

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

boydman_xm@mail.zjxu.edu.cn (Yubo Yang)

hpma@shu.edu.cn (Heping Ma)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-629, author = {Yang , Yubo and Ma , Heping}, title = {A Linear Implicit L1-Legendre Galerkin Chebyshev Collocation Method for Generalized Time- and Space-Fractional Burgers Equation}, journal = {Journal of Computational Mathematics}, year = {2019}, volume = {37}, number = {5}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1807-m2017-0197}, url = {http://global-sci.org/intro/article_detail/jcm/13038.html} }
TY - JOUR T1 - A Linear Implicit L1-Legendre Galerkin Chebyshev Collocation Method for Generalized Time- and Space-Fractional Burgers Equation AU - Yang , Yubo AU - Ma , Heping JO - Journal of Computational Mathematics VL - 5 SP - 629 EP - 644 PY - 2019 DA - 2019/03 SN - 37 DO - http://doi.org/10.4208/jcm.1807-m2017-0197 UR - https://global-sci.org/intro/article_detail/jcm/13038.html KW - Generalized fractional Burgers equation, Stability and convergence analysis, Legendre Galerkin Chebyshev collocation method, Finite difference method. AB -

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.

Yang , Yubo and Ma , Heping. (2019). A Linear Implicit L1-Legendre Galerkin Chebyshev Collocation Method for Generalized Time- and Space-Fractional Burgers Equation. Journal of Computational Mathematics. 37 (5). 629-644. doi:10.4208/jcm.1807-m2017-0197
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