A LINEAR IMPLICIT L1-LEGENDRE GALERKIN CHEBYSHEV COLLOCATION METHOD FOR GENERALIZED TIME-AND SPACE-FRACTIONAL BURGERS EQUATION

• 来源期刊: 计算数学（英文版）
• 关键词: Generalized fractional Burgers equation Stability and convergence analysis Legendre Galerkin Chebyshev collocation method Finite difference method
• 年，卷（期）: 2019,（5）
• 页码范围: 629-644
• 页数: 16页
• 语种: 英文
• DOI: 10.4208/jcm.1807-m2017-0197

摘要

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.