求解时间分布阶扩散方程的两个高阶有限差分格式  

Two High-Order Difference Schemes for Solving Time Distributed-Order Diffusion Equations

作　　者：胡嘉卉 王俊刚[1] 聂玉峰[1] HU Jiahui;WANG Jungang;NIE Yufeng(Department of Applied Mathematics,Northwestern Polytechnical University,Xi’an 710129,P.R.China;School of Sciences,Henan University of Technology,Zhengzhou 450001,P.R.China)

机构地区：[1]西北工业大学应用数学系,西安710129 [2]河南工业大学理学院,郑州450001

出　　处：《应用数学和力学》2019年第7期791-800,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11471262)~~

摘　　要：基于复化Simpson公式和复化两点Gauss-Legendre公式,构造了两个求解时间分布阶扩散方程的高阶有限差分格式.不同于以往文献中提出的时间一阶或二阶格式,这两种格式在时间方向都具有三阶精度,而在分布阶和空间方向可达到四阶精度.数值结果表明,两种算法都是稳定且收敛的,从而是有效的.两种格式的收敛速率也通过数值实验进行了验证,并且通过和文献中的算法对比可以得出其更为高效.Based on the composite Simpson’ s quadrature rule and the composite 2-point Gauss-Legendre quadrature rule, 2 high-order finite difference schemes were proposed for solving time distributed-order diffusion equations. Other than the existing methods whose convergence rates are only 1st-order or 2nd-order in the temporal domain, the proposed 2 schemes both have 3rd-order convergence rates in the temporal domain, and 4th-order rates in the spatial domain and the distributed order, respectively. Such high-order convergence rates were further verified with numerical examples. The results show that, both of the proposed 2 schemes are stable, and have higher accuracy and efficiency compared with existing algorithms.

关 键 词：时间分布阶扩散方程 分数阶导数 高阶差分格式 收敛速率 

分 类 号：O242.2[理学—计算数学]