Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral
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,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Saratov State University
2021-05-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| Subjects: | |
| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/05/151-161lukomskii-lukomskii.pdf |
| Summary: | 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. |
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| ISSN: | 1816-9791 2541-9005 |