THE CONCEPT OF THE INVERSE PROBLEM OF DIFFERENTIAL EQUATIONS
The purpose of the article is to reveal the problems in solving inverse and ill-posed problems with given differential equations. When studying any physical phenomenon, the researcher first of all creates its mathematical idealization or, in other words, a mathematical model, that is, neglecting the...
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K.Tynystanov Issyk-Kul State University
2025-03-01
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| Series: | Vestnik Issyk-Kulʹskogo universiteta |
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| Online Access: | https://api.libraryiksu.kg/vestnik/ISUASKERBEKOVA, DYUSHEBAEVA61-202557100.pdf |
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| author | Askerbekova A. Dyushebaeva A. |
| author_facet | Askerbekova A. Dyushebaeva A. |
| author_sort | Askerbekova A. |
| collection | DOAJ |
| description | The purpose of the article is to reveal the problems in solving inverse and ill-posed problems with given differential equations. When studying any physical phenomenon, the researcher first of all creates its mathematical idealization or, in other words, a mathematical model, that is, neglecting the secondary characteristics of the phenomenon, he writes down the basic laws governing this phenomenon in mathematical form. Very often these laws can be expressed in the form of differential equations.
The authors emphasize the main features and fundamental concepts of correct and incorrect problems of mathematical physics. In addition, a review and classification of inverse problems of mathematical physics is presented. A number of examples of correct and incorrect problems are given. A review of methods for solving such problems is given. |
| format | Article |
| id | doaj-art-8a95bc9500e34ebb96997df521ef0474 |
| institution | OA Journals |
| issn | 1561-9516 1694-8211 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | K.Tynystanov Issyk-Kul State University |
| record_format | Article |
| series | Vestnik Issyk-Kulʹskogo universiteta |
| spelling | doaj-art-8a95bc9500e34ebb96997df521ef04742025-08-20T02:36:30ZengK.Tynystanov Issyk-Kul State UniversityVestnik Issyk-Kulʹskogo universiteta1561-95161694-82112025-03-0161916https://doi.org/10.69722/1694-8211-2025-61-9-16THE CONCEPT OF THE INVERSE PROBLEM OF DIFFERENTIAL EQUATIONSAskerbekova A.0https://orcid.org/0009-0001-0399-4202Dyushebaeva A.1https://orcid.org/0009-0004-2756-9587K. Tynystanov Issyk-Kul state universityK. Tynystanov Issyk-Kul state universityThe purpose of the article is to reveal the problems in solving inverse and ill-posed problems with given differential equations. When studying any physical phenomenon, the researcher first of all creates its mathematical idealization or, in other words, a mathematical model, that is, neglecting the secondary characteristics of the phenomenon, he writes down the basic laws governing this phenomenon in mathematical form. Very often these laws can be expressed in the form of differential equations. The authors emphasize the main features and fundamental concepts of correct and incorrect problems of mathematical physics. In addition, a review and classification of inverse problems of mathematical physics is presented. A number of examples of correct and incorrect problems are given. A review of methods for solving such problems is given.https://api.libraryiksu.kg/vestnik/ISUASKERBEKOVA, DYUSHEBAEVA61-202557100.pdfdifferential equationsinverse problemincorrect taskinitial conditionboundary conditionproblem modelsolution of equationapproximate methodsnumerical methodscauchy problemdifferential operatorintegralsystem of equationsexact solution |
| spellingShingle | Askerbekova A. Dyushebaeva A. THE CONCEPT OF THE INVERSE PROBLEM OF DIFFERENTIAL EQUATIONS Vestnik Issyk-Kulʹskogo universiteta differential equations inverse problem incorrect task initial condition boundary condition problem model solution of equation approximate methods numerical methods cauchy problem differential operator integral system of equations exact solution |
| title | THE CONCEPT OF THE INVERSE PROBLEM OF DIFFERENTIAL EQUATIONS |
| title_full | THE CONCEPT OF THE INVERSE PROBLEM OF DIFFERENTIAL EQUATIONS |
| title_fullStr | THE CONCEPT OF THE INVERSE PROBLEM OF DIFFERENTIAL EQUATIONS |
| title_full_unstemmed | THE CONCEPT OF THE INVERSE PROBLEM OF DIFFERENTIAL EQUATIONS |
| title_short | THE CONCEPT OF THE INVERSE PROBLEM OF DIFFERENTIAL EQUATIONS |
| title_sort | concept of the inverse problem of differential equations |
| topic | differential equations inverse problem incorrect task initial condition boundary condition problem model solution of equation approximate methods numerical methods cauchy problem differential operator integral system of equations exact solution |
| url | https://api.libraryiksu.kg/vestnik/ISUASKERBEKOVA, DYUSHEBAEVA61-202557100.pdf |
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