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具有收敛分析的谱方法求解一维和二维混合 Volterra-Fredholm 积分方程。

Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation.

机构信息

Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan, Malaysia, Malaysia.

Department of Basic Sciences, Adham University College, Umm AL-Qura University, Makkah, Saudi Arabia.

出版信息

PLoS One. 2023 May 26;18(5):e0283746. doi: 10.1371/journal.pone.0283746. eCollection 2023.

DOI:10.1371/journal.pone.0283746
PMID:37235577
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10218756/
Abstract

A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredholm integral equations to a system of algebraic equations that has an easy solved. The present algorithm is extended to solve the one and two-dimensional mixed Volterra-Fredholm integral equations. Convergence analysis for the present method is discussed and confirmed the exponential convergence of the spectral algorithm. Various numerical examples are approached to demonstrate the powerful and accuracy of the technique.

摘要

提出了一种基于移位 Jacobi-Gauss 配点法求解混合 Volterra-Fredholm 积分方程的数值方法。该技术利用移位 Jacobi-Gauss 节点将混合 Volterra-Fredholm 积分方程降阶为易于求解的代数方程组。将该算法推广到求解一维和二维混合 Volterra-Fredholm 积分方程。讨论了该方法的收敛性分析，并验证了谱算法的指数收敛性。通过各种数值实例验证了该技术的有效性和准确性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/33f2/10218756/d11b06d6fe7c/pone.0283746.g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/33f2/10218756/4c3544c20d1d/pone.0283746.g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/33f2/10218756/3808551c31ba/pone.0283746.g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/33f2/10218756/fefccf4c86e3/pone.0283746.g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/33f2/10218756/d11b06d6fe7c/pone.0283746.g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/33f2/10218756/4c3544c20d1d/pone.0283746.g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/33f2/10218756/3808551c31ba/pone.0283746.g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/33f2/10218756/fefccf4c86e3/pone.0283746.g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/33f2/10218756/d11b06d6fe7c/pone.0283746.g004.jpg

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