弱奇异核积分微分方程的样条准插值数值方法

IF 1.6 3区 数学 Q1 MATHEMATICS Mathematical Modelling and Analysis Pub Date : 2024-05-21 DOI:10.3846/mma.2024.18832
A. Saou, D. Sbibih, M. Tahrichi, Domingo Barrera
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引用次数: 0

摘要

在这项工作中,我们介绍了一种利用有界区间上的花键准插值算子的数值方法。该方法旨在为一类具有弱奇异内核的弗雷德霍尔姆积分微分方程提供数值解。我们概述了确定近似解所涉及的计算部分,并提供了有关收敛速率的理论发现。我们分析了收敛速度与准内插数度和分级网格划分的分级指数的关系。最后,我们介绍了验证理论结论的数值实验。
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SPLINE QUASI-INTERPOLATION NUMERICAL METHODS FOR INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS
In this work, we introduce a numerical approach that utilizes spline quasi-interpolation operators over a bounded interval. This method is designed to provide a numerical solution for a class of Fredholm integro-differential equations with weakly singular kernels. We outline the computational components involved in determining the approximate solution and provide theoretical findings regarding the convergence rate. This convergence rate is analyzed in relation to both the degree of the quasi-interpolant and the grading exponent of the graded grid partition. Finally, we present numerical experiments that validate the theoretical findings.
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来源期刊
CiteScore
2.80
自引率
5.60%
发文量
28
审稿时长
4.5 months
期刊介绍: Mathematical Modelling and Analysis publishes original research on all areas of mathematical modelling and analysis.
期刊最新文献
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