求解震荡型矩阵函数的一类有效数值算法  

An Efficient Numerical Algorithm for Solving Oscillating Matrix Function

作　　者：王楠 杨思宇 李东平 WANG Nan;YANG Si-yu;LI Dong-ping(College of Mathematics,Changchun Normal University,Changchun 130032,China)

机构地区：[1]长春师范大学数学学院,吉林长春130032

出　　处：《长春师范大学学报》2023年第4期13-18,共6页Journal of Changchun Normal University

基　　金：长春师范大学自然科学基金项目“基于指数积分方法的大型矩阵微分方程高性能算法研究”(202101)。

摘　　要：震荡型矩阵函数主要出现在求解二阶半线性常微分方程的ERKN积分中,其计算效率直接决定了这类积分的计算效率.本文设计了修正的缩放四次方方法求解震荡型矩阵函数,基于后验误差分析理论提取了关键参数.数值实验表明了该方法的有效性和稳定性.The oscillating matrix function mainly appears in ERKN integrals for solving second order semi-linear ordinary differential equations.Its computational efficiency directly determines the computational efficiency of such integrals.In this paper,a modified scaling fourth power method is designed to solve the oscillating matrix function.The key parameters of the method are extracted based on quasi-backward error analysis theory.Numerical experiments show the effectiveness and stability of the proposed method.

关 键 词：震荡型矩阵函数 ERKN积分法 准向后误差分析 

分 类 号：O242.2[理学—计算数学]