Volume 11, Issue 2
The Legendre Galerkin-Chebyshev Collocation Method for Space Fractional Burgers-Like Equations

Yubo Yang & Heping Ma

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 338-353.

Published online: 2018-11

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  • Abstract

In this paper, a Legendre Galerkin Chebyshev collocation method for the Burgers-like equations with fractional nonlinear term and diffusion term is developed. This method is based on the Legendre-Galerkin variational form, but the nonlinear term and the right-hand term are treated by Chebyshev-Gauss interpolation. Rigorous stability and convergence analysis are developed. Numerical examples are shown to demonstrate the accuracy, stability and effectiveness of this method.

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@Article{NMTMA-11-338, author = {}, title = {The Legendre Galerkin-Chebyshev Collocation Method for Space Fractional Burgers-Like Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {2}, pages = {338--353}, abstract = {

In this paper, a Legendre Galerkin Chebyshev collocation method for the Burgers-like equations with fractional nonlinear term and diffusion term is developed. This method is based on the Legendre-Galerkin variational form, but the nonlinear term and the right-hand term are treated by Chebyshev-Gauss interpolation. Rigorous stability and convergence analysis are developed. Numerical examples are shown to demonstrate the accuracy, stability and effectiveness of this method.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0087}, url = {http://global-sci.org/intro/article_detail/nmtma/12433.html} }
TY - JOUR T1 - The Legendre Galerkin-Chebyshev Collocation Method for Space Fractional Burgers-Like Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 338 EP - 353 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0087 UR - https://global-sci.org/intro/article_detail/nmtma/12433.html KW - AB -

In this paper, a Legendre Galerkin Chebyshev collocation method for the Burgers-like equations with fractional nonlinear term and diffusion term is developed. This method is based on the Legendre-Galerkin variational form, but the nonlinear term and the right-hand term are treated by Chebyshev-Gauss interpolation. Rigorous stability and convergence analysis are developed. Numerical examples are shown to demonstrate the accuracy, stability and effectiveness of this method.

Yubo Yang & Heping Ma. (2020). The Legendre Galerkin-Chebyshev Collocation Method for Space Fractional Burgers-Like Equations. Numerical Mathematics: Theory, Methods and Applications. 11 (2). 338-353. doi:10.4208/nmtma.OA-2017-0087
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