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

Yubo Yang & Heping Ma

DOI: 10.4208/nmtma.OA-2017-0087

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 = {Yubo Yang and Heping Ma}, 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 AU - Yubo Yang & Heping Ma 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 and Heping Ma. (2018). 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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