求解第二类完全超奇异积分方程的数值方法及其证明

IF 1.6 3区数学 Q1 MATHEMATICS

Mathematical Modelling and Analysis Pub Date : 2023-10-20 DOI:10.3846/mma.2023.14761

Oleksii V. Kostenko

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引用次数: 0

摘要

得到了一个完整的第二类超奇异积分方程，作为电磁波在周期性放置的非完美导电带分隔的空间中的衍射和散射问题的边界积分方程。该方程包含一个奇异积分，使其区别于所研究的第二类超奇异方程。我们的动机是需要有一个方程的数值方法，它的适用性边界，并保证收敛。数值方法的类型为Nyström。该方法的证明包括解的存在唯一性定理的证明和精确解的近似解序列的收敛速率的估计。

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A NUMERICAL METHOD FOR SOLVING A COMPLETE HYPERSINGULAR INTEGRAL EQUATION OF THE SECOND KIND AND ITS JUSTIFICATION

A complete hypersingular integral equation of the second kind was obtained as a boundary integral equation for the diffraction and scattering problem of electromagnetic waves in space separated by the periodically placed non-perfectly conducting strips. The equation includes a singular integral that distinguishes it from the studied second-kind hypersingular equation. Our motivation is the need to have a numerical method for the equation, its applicability borders, and guaranteed convergence. The numerical method has the type of Nyström. The justification of the method envelops a proof of the theorem of existence and uniqueness of the solution and an estimate of the convergence rate of sequence of the approximate solutions to an exact solution.

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来源期刊

Mathematical Modelling and Analysis 数学-数学

CiteScore

2.80

自引率

5.60%

发文量

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.