Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Lukomskii S. F., Lukomskii D. S. Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 2, pp. 151-161. DOI: 10.18500/1816-9791-2021-21-2-151-161, EDN: WJTAJG

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.05.2021
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English
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Article
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517.926
EDN: 
WJTAJG

Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral

Autors: 
Lukomskii Sergei Feodorovich, Saratov State University
Lukomskii Dmitry Sergeyevich, Saratov State University
Abstract: 

We consider the  problem of approximate solution of linear differential equations with discontinuous coefficients. We assume that  these coefficients have $f$-primitive. It means that  these coefficients are Henstock integrable only. Instead of the original Cauchy problem,  we consider a different problem with piecewise-constant coefficients. The sharp solution of this new problem is the approximate solution of the original Cauchy problem. We found the degree of approximation in terms of $f$-primitive for Henstock integrable coefficients. Two examples are given. In the first example, the coefficients have an infinite derivative at zero. In the second example, the coefficients have an infinite derivative at interior points.

Acknowledgments: 
First author was supported by Education Center “Mathematics of Future Technologies”.
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Received: 
17.03.2020
Accepted: 
07.10.2020
Published: 
31.05.2021