摘要
In this paper, a linear implicit Ll-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 L 1-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.
基金
We are grateful to the referees and the editor for their valuable suggestions and help in improving the presentation. The work of the first author has been supported by National Natural Science Foundation of China (11571225)
Zhejiang Provincial Natural Science Foundation of China (LY15A010018)
the Key Research Project of Nanhu College, Jiaxing University (N41472001-29)
The work of the second author has been supported by National Natural Science Foundation of China (11571224).
