Generalized Clenshaw-Curtis quadrature method for systems of linear ODEs with constant coefficients

IF 2.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2025-06-09 DOI:10.1016/j.apnum.2025.06.003

Fu-Rong Lin, Xi Yang, Gui-Rong Zhang

引用次数: 0

Abstract

In this paper, we consider high precision numerical methods for the initial problem of systems of linear ordinary differential equations (ODEs) with constant coefficients. It is well-known that the analytic solution of such a system of linear ODEs involves a matrix exponential function and an integral whose integrand is the product of a matrix exponential and a vector-valued function. We mainly consider numerical quadrature methods for the integral term in the analytic solution and propose a generalized Clenshaw-Curtis (GCC) quadrature method. The proposed method is then applied to the initial-boundary value problem for a heat conduction equation and a Riesz space fractional diffusion equation, respectively. Numerical results are presented to demonstrate the effectiveness of the proposed method.

查看原文本刊更多论文

常系数线性微分方程系统的广义Clenshaw-Curtis正交法

本文研究了常系数线性常微分方程系统初始问题的高精度数值解法。众所周知，这种线性微分方程系统的解析解涉及一个矩阵指数函数和一个积分，其被积是一个矩阵指数函数和一个向量值函数的乘积。本文主要研究了解析解中积分项的数值求积分方法，提出了一种广义的clclenshaw - curtis求积分方法。然后将该方法分别应用于热传导方程和Riesz空间分数扩散方程的初边值问题。数值结果验证了该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.