Local error estimate of L1 scheme for linearized time fractional KdV equation with weakly singular solutions

被引：5
|
作者：
Chen, Hu [1 ]
Chen, Mengyi [2 ]
Sun, Tao [3 ]
Tang, Yifa [2 ,4 ]
机构：
[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China
[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[3] Shanghai Lixin Univ Accounting & Finance, Sch Stat & Math, Shanghai 201209, Peoples R China
[4] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2022年 / 179卷
基金：
中国国家自然科学基金;
关键词：
L1; scheme; Time-fractional KdV equation; Local error estimate; Weakly singular solution; GALERKIN METHOD; GRADED MESHES;
D O I：
10.1016/j.apnum.2022.04.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the local error estimate of the L1 scheme on graded mesh for a linearized time fractional KdV equation with weakly singular solutions, where Legendre Petrov-Galerkin spectral method is used for the spatial discretization. Stability and convergence of the fully discrete scheme are rigorously established, and the pointwise-in-time error estimates are given to show that one can attain the optimal convergence order 2 - alpha in positive time by mildly choosing the grading parameter r no more than 2 for all 0 < alpha < 1. Numerical results are presented to show that the error estimate is sharp. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.
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页码：183 / 190
页数：8
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