METHOD FOR SOLVING ILL-POSED PROBLEMS FOR DIFFERENTIAL EQUATIONS WITH APPROXIMATELY GIVEN FUNCTIONS BASED ON THE REPRESENTATION OF THE SOLUTION OF INTEGRAL EQUATIONS
The work outlines a method of constructing an approximate solution of the differential equation with the initial data obtained in the experiment (empirical functions), which are known with some errors. In such statement the problem belongs to the class of incorrect mathematical problems and often oc...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | Russian |
| Published: |
North-Caucasus Federal University
2022-09-01
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| Series: | Наука. Инновации. Технологии |
| Subjects: | |
| Online Access: | https://scienceit.elpub.ru/jour/article/view/363 |
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| Summary: | The work outlines a method of constructing an approximate solution of the differential equation with the initial data obtained in the experiment (empirical functions), which are known with some errors. In such statement the problem belongs to the class of incorrect mathematical problems and often occurs, for example, in mathematical models of physical phenomena using measurement results of field experiments. This is due to the relevance of the research. To obtain the approximate solution of this problem requires construction of appropriate regularization algorithms based on the methods of the theory of functional analysis and ill-posed problems. In the present work is the construction of the approximate solution of odes with specified boundary conditions, are the so-called singular integrals. This allows you to put in the original equation Fredholm integral equation of the first kind and to find its numerical solution. This uses a machine approximation of functions and their derivatives corresponding singular integrals and regularization method convergence of the sequence of approximate solutions, which implemented the so-called generalized inverse operators. Built in the end, a computational model allows to obtain a stable solution of ill-posed problems. |
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| ISSN: | 2308-4758 |