变指数权函数积分的高斯积分规则及其在弱奇异Volterra积分方程中的应用

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

IMA Journal of Numerical Analysis Pub Date : 2025-01-23 DOI:10.1093/imanum/drae088

Chafik Allouch, Gradimir V Milovanović

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引用次数: 0

摘要

本文提出了一种数值积分方法，可用于在有限区间内逼近含有可变指数雅可比权值的函数的积分。需要对被积函数进行接近奇异点的修正，并提出了一种新的修正。并探讨了该规则在第二类变指数弱奇异Volterra积分方程数值解中的应用。在连续函数空间中，证明了该方法的稳定性和误差估计，并进行了数值试验验证。

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Gauss quadrature rules for integrals involving weight functions with variable exponents and an application to weakly singular Volterra integral equations

This paper presents a numerical integration approach that can be used to approximate on a finite interval, the integrals of functions that contain Jacobi weights with variable exponents. A modification of the integrand close to the singularities is needed, and a new modification is proposed. An application of such a rule to the numerical solution of variable-exponent weakly singular Volterra integral equations of the second kind is also explored. In the space of continuous functions, the stability and the error estimates are demonstrated, and numerical tests that validate these estimates are conducted.

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来源期刊

IMA Journal of Numerical Analysis 数学-应用数学

CiteScore

5.30

自引率

4.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.