On the numerical solution of highly oscillatory Fredholm integral equations using a generalized quadrature method

被引：0

作者：

Jhaily, Adil Owaid ^{[1
]}

Sohrabi, Saeed ^{[1
]}

Ranjbar, Hamid ^{[1
]}

机构：

[1] Urmia Univ, Fac Sci, Dept Math, Orumiyeh 5756151818, Iran

来源：

AIMS MATHEMATICS | 2025年 / 10卷 / 03期

关键词：

highly oscillatory; integral equation; asymptotic order; convergence; FILON-TYPE METHODS; COLLOCATION METHODS; KIND;

D O I：

10.3934/math.2025260

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a numerical method is presented for solving Fredholm integral equations with highly oscillatory kernels. The proposed method combined piecewise collocation with a generalized quadrature rule in a uniform mesh. Due to the oscillatory nature of the kernels of integral equation, the discretized collocation equations required the evaluation of oscillatory integrals, which were computed using an efficient generalized quadrature rule. Convergence was analyzed in terms of both asymptotic and classical accuracy. The method's practical performance and reliability were showcased with two numerical examples.

引用

页码：5631 / 5650

页数：20

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