求解二维Hammerstein积分方程的超收敛方法

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-09-22 DOI:10.1016/j.amc.2025.129737

M. Sennour , D. Sbibih , M. Tahrichi

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引用次数: 0

摘要

本文介绍了二维第二类Hammerstein积分方程数值解的超收敛退化核方法和超收敛Nyström方法。利用r次分段多项式插值，证明了在三角剖分节点和插值节点均对称的条件下，近似解及其迭代版本的收敛阶分别为2r+3和2r+4。此外，我们讨论了与相应的非线性系统的构造有关的计算方面，并给出了数值例子来说明所得到的理论结果。

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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Superconvergent methods for solving two-dimensional Hammerstein integral equations

In this paper, we introduce the superconvergent degenerate kernel method and the superconvergent Nyström method for the numerical solution of two-dimensional Hammerstein integral equations of the second kind. By employing piecewise polynomial interpolation of degree

r

, we prove that, under symmetry conditions on both the triangulation and the interpolation nodes, convergence orders of

2 r + 3

and

2 r + 4

are achieved for the approximate solutions and their iterated versions, respectively. Furthermore, we discuss computational aspects related to the construction of the corresponding nonlinear systems, and we present numerical examples to illustrate the theoretical results obtained.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.