Numerical Solution of Integral Equations of the Third Kind withFixed Singularities of the Kernel

A linear integral equation of the third kind with fixed singularities in the kernel is studied. For its approximate solution in the space of generalized functions, a special generalized spline method is proposed and substantiated. Optimality of the method in the order of accuracy is proved.

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Publication Details

Journal
Differential Equations
Published
2025-05-01
DOI
https://doi.org/10.1134/s001226612505012x
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

Numerical Solution of Integral Equations of the Third Kind withFixed Singularities of the Kernel

Differential Equations
Geochemistry and Geologic Mapping
article

Numerical Solution of Integral Equations of the Third Kind withFixed Singularities of the Kernel

article en

Abstract

A linear integral equation of the third kind with fixed singularities in the kernel is studied. For its approximate solution in the space of generalized functions, a special generalized spline method is proposed and substantiated. Optimality of the method in the order of accuracy is proved.

Differential EquationsVol. 61(5)
Naberezhnye Chelny State Pedagogical Institute (RU)
Openalex Percentile: Top 26%
Geochemistry and Geologic Mapping
DOISourceOpenAlex
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Numerical Solution of Integral Equations of the Third Kind withFixed Singularities of the Kernel · Differential Equations (2025) | TGRS Research Map | TGRS