数值计算与计算机应用
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数值计算与计算机应用  2017, Vol. 38 Issue (3): 236-244    DOI:
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广义空间分数阶Burgers方程的Legendre Galerkin-Chebyshev配置方法逼近
杨宇博1,2, 马和平1
1. 上海大学理学院数学系, 上海 200444;
2. 嘉兴学院南湖学院数理与信息工程系, 嘉兴 314001
THE LEGENDRE GALERKIN-CHEBYSHEV COLLOCATION METHOD FOR GENERALIZED SPACE-FRACTIONAL BURGERS EQUATIONS
Yang Yubo1,2, Ma Heping1
1. Department of Mathemactics, College of Sciences, Shanghai University, Shanghai 200444, China;
2. Department of Mathematics, Physics and Information Engineering, Nanhu College, Jiaxing University, Jiaxing 314001, China
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摘要 本文采用Legendre Galerkin-Chebyshev配置方法求解广义空间分数阶Burgers方程.该方法基于Legendre Galerkin变分形式,但是非线性项与右端源项采用Chebyshev-Gauss插值逼近.首先,通过在空间方向采用Legendre Galerkin-Chebyshev配置方法离散,时间方向采用leap-frog/Crank-Nicolson格式离散,得到了方程的全离散格式,其中非线性项能够显式计算.接着,给出了稳定性分析及L2-范数下的误差估计.数值算例显示该方法的稳定性,高效性及易实现性.
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关键词广义空间分数阶Burgers方程   Legendre Galerkin-Chebyshev配置方法   误差估计     
Abstract: In this paper, the Legendre Galerkin-Chebyshev collocation method is developed to solve the generalized space-fractional Burgers equations. This method is based on the Legendre Galerkin variational form, but the nonlinear term and right-hand source term are approximated by the Chebyshev-Gauss interpolation. Firstly, the Legendre Galerkin-Chebyshev collocation method and the leap-frog/Crank-Nicolson scheme are used in spatial and temporal dicretization respectively, which lead to the fully discrete scheme with explicit computation of the nonlinear term. Then, the stability and error estimate in the L2-norm are established respectively. Numerical examples show that this method is stable, efficient and easy to implement.
Key wordsgeneralized space-fractional Burgers equations   Legendre Galerkin-Chebyshev collocation method   error estimate   
收稿日期: 2016-10-30;
基金资助:

国家自然科学基金(11571224,11571225),浙江省自然科学基金(LY15A010018)和嘉兴学院南湖学院科研重点项目(N41472001-29)资助.

引用本文:   
. 广义空间分数阶Burgers方程的Legendre Galerkin-Chebyshev配置方法逼近[J]. 数值计算与计算机应用, 2017, 38(3): 236-244.
. THE LEGENDRE GALERKIN-CHEBYSHEV COLLOCATION METHOD FOR GENERALIZED SPACE-FRACTIONAL BURGERS EQUATIONS[J]. Journal of Numerical Methods and Computer Applicat, 2017, 38(3): 236-244.
 
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