Efficient mapped Jacobi spectral method for integral equations with two-sided singularities

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-08-10 DOI:10.1016/j.apnum.2024.08.003

Xiu Yang , Changtao Sheng

引用次数: 0

Abstract

In this paper, we develop a mapped Jacobi spectral Galerkin method for solving the multi-term Fredholm integral equations (MFIEs) with two-sided weakly singularities. We introduce a new family of mapped Jacobi functions (MJFs) and establish the corresponding spectral approximation results on these MJFs in weighted Sobolev spaces involving the mapped Jacobi weight function. These MJFs serve as the basis functions in our algorithm design and are tailored to the two-sided end-points singularities of the solution by using suitable mapping. Moreover, we derive the error estimates of the proposed method for MFIEs. Finally, the numerical examples are provided to demonstrate the accuracy and efficiency of the proposed method.

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具有双面奇点的积分方程的高效映射雅可比谱法

本文开发了一种映射雅可比谱 Galerkin 方法，用于求解具有双面弱奇点的多期弗雷德霍姆积分方程（MFIEs）。我们引入了新的映射雅可比函数（MJFs）族，并在涉及映射雅可比权函数的加权索波列夫空间中建立了这些 MJFs 的相应谱近似结果。这些 MJF 在我们的算法设计中用作基函数，并通过适当的映射来适应解的双侧端点奇异性。此外，我们还推导了所提方法对 MFIE 的误差估计。最后，我们提供了数值示例来证明所提方法的准确性和高效性。

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

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.