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一类空间分数阶Burgers方程守恒型差分方法
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Abstract:
本文采用守恒型差分方法求解一类空间分数阶Buegers方程，其中时间方向和空间方向分别采用Crank-Nicolson格式和有限差分法离散。实验结果表明，该方法在时间和空间上的收敛速度都为二阶。
This paper develops a conservative discretization for a space-fractional Burgers equation, in which the temporal Crank-Nicolson scheme and spacial finite difference method are used. Numerical test shows that the convergence of this method is of order 2 in time and space.
| [1] | Sugimoto, N. (1991) Burgers Equation with a Fractional Derivative; Hereditary Effects on Nonlinear Acoustic Waves. Journal of Fluid Mechanics, 225, 631-653. https://doi.org/10.1017/S0022112091002203 |
| [2] | Wu, Q. and Zeng, X. (2020) Jacobi Collocation Methods for Solving Generalized Space-Fractional Burgers Equations. Communications on Applied Mathematics and Computation, 2, 305-318. https://doi.org/10.1007/s42967-019-00053-6 |
| [3] | 杨宇博, 马和平. 广义空间分数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. |
| [4] | Dimitrov, Y. (2015) A Second Order Approximation for Caputo Fractional Derivative.
https://arxiv.org/abs/1502.00719 |
| [5] | Hesthaven, J.S. (2017) Chapter 4: From Continuous to Discrete. In: Numerical Methods for Conservation Laws.
https://doi.org/10.1137/1.9781611975109.ch4 |
