A quadrature method for Volterra integral equations with highly oscillatory Bessel kernel

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2024-09-05 DOI:10.1016/j.matcom.2024.09.002

Longbin Zhao , Pengde Wang , Qiongqi Fan

引用次数: 0

Abstract

To avoid computing moments, this work adopts generalized quadrature method for Volterra integral equations with highly oscillatory Bessel kernel. At first, we study the influence of the interval length and frequency in detail after recalling the construction of the quadrature method. Then, the two-point quadrature method is employed for the equation. By estimating the weights, we could guarantee that the discretized equation is solvable. For its convergence, our analysis shows that the proposed method enjoys asymptotic order $5 / 2$ and as $h$ decreases it converges with order 2 as well. Some numerical illustrations are provided to test the method in the numerical part.

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具有高振荡贝塞尔核的 Volterra 积分方程的正交方法

为了避免计算矩，本研究采用广义正交法来求解具有高振荡贝塞尔核的 Volterra 积分方程。首先，我们在回顾正交方法的构造后，详细研究了区间长度和频率的影响。然后，对方程采用两点正交法。通过估计权重，我们可以保证离散方程是可解的。在收敛性方面，我们的分析表明，所提出的方法具有 5/2 的渐近阶，随着 h 的减小，其收敛阶数也为 2。在数值部分，我们提供了一些数值示例来检验该方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

期刊介绍： The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.