A second-order accurate numerical method with graded meshes for an evolution equation with a weakly singular kernel

被引：41
|
作者：
Chen, Hongbin [1 ]
Xu, Da [2 ]
Zhou, Jun [2 ,3 ]
机构：
[1] Cent South Univ Forestry & Technol, Coll Sci, Inst Math & Phys, Changsha 410004, Hunan, Peoples R China
[2] Hunan Normal Univ, Sch Math & Stat, Minist Educ, Key Lab Comp & Stochast Math, Changsha 410081, Hunan, Peoples R China
[3] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 356卷
基金：
中国国家自然科学基金;
关键词：
Evolution equation; Weakly singular kernel; Graded meshes; Generalized Crank-Nicolson method; Compact difference scheme; DIFFERENCE SCHEME; INTEGRODIFFERENTIAL EQUATIONS; DIFFUSION EQUATION; ERROR ANALYSIS; HEAT-EQUATION; DISCRETIZATION; COLLOCATION;
D O I：
10.1016/j.cam.2019.01.031
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A second-order accurate numerical method with graded meshes is proposed and analyzed for an evolution equation with a weakly singular kernel. The graded meshes are employed to compensate for the singular behavior of the exact solution at t = 0. For the time discretization, the product integration rule is used to approximate the Riemann-Liouville fractional integral, a generalized Crank-Nicolson time-stepping is considered and shown that the error is of order k(2), where k denotes the maximum time step. A fully discrete difference scheme is constructed with space discretization by compact difference method. Numerical experiment is carried out to support the theoretical results. The comparison between the method on uniform grids and graded grids shows the efficiency of our method. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：152 / 163
页数：12
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