A Linear Implicit L1-Legendre Galerkin Chebyshev Collocation Method for Generalized Time- and Space-Fractional Burgers Equation
A Linear Implicit L1-Legendre Galerkin Chebyshev Collocation Method for Generalized Time- and Space-Fractional Burgers Equation
复制标题
广义时空分式Burgers方程的线性隐式L1-Legendre Galerkin Chebyshev配置方法
DOI：
10.4208/jcm.1807-m2017-0197
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发表时间：
2019-06
影响因子：
0.9
通讯作者：
Ma Heping
中科院分区：
文献类型：
--
作者：
Yang Yubo;Ma Heping
本文对广义时空分数阶Burgers方程提出了一种线性隐式L1-Legendre Galerkin Chebyshev配置方法。提出了一种基于L1算法的Caputo分数阶导数的线性隐式差分格式。基于Legendre-Galerkin变分形式，提出了Legendre-Galerkin Chebyshev配点法，但对非线性项和右手项采用Chebyshev-Gauss插值处理。严格的稳定性和收敛性分析。数值算例表明了该方法的准确性、稳定性和有效性。数学学科分类：65 M70、65 M12、65 M15、26 A33、35 R11。
In this paper, a linear implicit L1-Legendre Galerkin Chebyshev collocation method for the generalized timeand 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. Mathematics subject classification: 65M70, 65M12, 65M15, 26A33, 35R11.