求解弱奇异高振荡傅立叶核或艾里核Volterra积分方程的有效配位方法

IF 1.7 4区数学 Q2 MATHEMATICS, APPLIED

International Journal of Computer Mathematics Pub Date : 2023-04-17 DOI:10.1080/00207160.2023.2203786

Jianyu Wang, Chunhua Fang, Gui-yu Zhang

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引用次数: 0

摘要

本文提出了直接线性插值配置法和直接高阶插值配置法两种配置方法，用于求解具有弱奇异高振荡傅立叶核或Airy核的第二类Volterra积分方程。目的是用Kummer超几何函数和Gamma函数求解修正矩方程，其中修正矩由积分区间[0,x]变换为积分区间[−1,1]。给出了具体的配置步骤，并通过收敛分析和数值实验证明了这些算法的有效性。通过数值算例证明了直接线性插值配置法和直接高阶插值配置法对于求解无弱奇点的高振荡方程也是有效的。

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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Effective collocation methods to solve Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels

In this paper two collocation methods, the direct linear interpolation collocation method and the direct high order interpolation collocation method, are proposed to solve the second kind of Volterra integral equations with weakly singular highly oscillatory Fourier or Airy kernels. The purpose is to solve the equations by Kummer hypergeometric and Gamma functions for solving the modified moments, where the modified moments are transformed from the integration interval [0,x] to the interval [−1,1]. The detailed collocation procedure is provided and the effectiveness of these algorithms are proved by convergence analysis and numerical experiments. Further, numerical examples are used to prove that the direct linear interpolation collocation method and the direct high order interpolation collocation method are also effective for solving highly oscillatory equations without weakly singularities.

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来源期刊

International Journal of Computer Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

5 months

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