What question did this study set out to answer?

This research aims to develop and verify numerical methods for solving singular integro-differential equations efficiently.

February 28, 2026

Order-Optimal Numerical Methods for Solving Singular Integro-Differential Equations

Key Points

This research aims to develop and verify numerical methods for solving singular integro-differential equations efficiently.
Studied linear integro-differential equation with a singular differential operator.
Proposed generalized methods of moments and subdomains for approximate solutions.
Analyzed solutions within the framework of generalized functions.
Established the optimality of the proposed methods regarding accuracy.
Demonstrated improved accuracy in solving singular integro-differential equations.

Abstract

A linear integro-differential equation with a singular differential operator in the principal part is studied. For its approximate solution in the space of generalized functions, special generalized versions of the methods of moments and subdomains are proposed and substantiated. Optimality of the methods in order of accuracy is established.

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Cite This Study

N. S. Gabbasov (Wed,) studied this question.

synapsesocial.com/papers/69a287a00a974eb0d3c037a3 https://doi.org/https://doi.org/10.7868/s3034533225110038

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