二维弱奇异 Volterra 第二类积分方程的广义对数正交函数谱配位法

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Numerical Methods for Partial Differential Equations Pub Date : 2024-04-29 DOI:10.1002/num.23105

Qiumei Huang, Min Wang

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引用次数: 0

摘要

本文提出了一种针对二维弱奇异 Volterra 第二类积分方程的广义对数正交函数（GLOFs）-谱配方法。高斯-GLOFs 正交法可以捕捉区间端点解的轻度奇异性，避免了传统谱法不能很好地处理具有有限正则解的弱奇异 Volterra 积分方程的缺点。对数值解进行了详细的收敛分析。通过数值示例证明了所提方法的高效性。

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Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind

In this article, a generalized log orthogonal functions (GLOFs)‐spectral collocation method to two dimensional weakly singular Volterra integral equations of the second kind is proposed. The mild singularities of the solution at the interval endpoint can be captured by Gauss‐GLOFs quadrature and the shortcoming of the traditional spectral method which cannot well deal with weakly singular Volterra integral equations with limited regular solutions is avoided. A detailed convergence analysis of the numerical solution is carried out. The efficiency of the proposed method is demonstrated by numerical examples.

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来源期刊

Numerical Methods for Partial Differential Equations 数学-应用数学

CiteScore

7.20

自引率

2.60%

发文量

审稿时长

9 months

期刊介绍： An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.