Modified Filon-type methods for second-order highly oscillatory systems with a time-dependent frequency matrix

被引：1
|
作者：
Liu, Zhongli [1 ]
Zhao, Hui [1 ]
Tian, Hongjiong [2 ,3 ]
机构：
[1] Shanghai Univ Int Business & Econ, Sch Stat & Informat, 1900 Wenxiang Rd, Shanghai 201620, Peoples R China
[2] Shanghai Normal Univ, Dept Math, 100 Guilin Rd, Shanghai 200234, Peoples R China
[3] Sci Comp Key Lab Shanghai Univ, 100 Guilin Rd, Shanghai 200234, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2023年 / 139卷
基金：
中国国家自然科学基金;
关键词：
equation; Time -dependent high frequency; Filon-type method; Waveform relaxation method; INTEGRATORS;
D O I：
10.1016/j.aml.2022.108540
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose a modified Filon-type method for solving second-order highly oscillatory systems with a time dependent matrix. We first transform the second-order problem into a first-order one and then integrate the transformed one by the Filontype method combined with the waveform relaxation method. The fundamental matrix in the formula of variation of constants can be calculated directly such that our proposed modified Filon-type method do not need to compute the nested integral commutators in the Magnus expansion. The global error of the modified Filon-type method is presented. Numerical examples show that our proposed numerical solver is efficient and accurate for highly oscillatory problems.(c) 2022 Elsevier Ltd. All rights reserved.
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