Керування наближеним розв'язком диференціальних рівнянь з розривними коефіцієнтами
Journal Title: Математичне моделювання - Year 2016, Vol 1, Issue 2
Abstract
ON CONTROL OF THE APPROXIMATE SOLUTION OF DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS COEFFICIENTS Dronov S.G. This study presents an algorithm for approximate solving of a marginal problem for the common second- order linear differential equations with discontinuous coefficients based using a non-uniform mesh cubic spline asymptotically converging with the interpolation spline of the exact solution. A special feature of this approach is that it guarantees an existence of the approximate solution and the possibility to control it. References [1] Zav'yalov Yu.S., Kvasov V.I., Miroshnichenko V.L. Metody splayn-funktsiy. M., 1980. [2] Korneychuk N.P. Splayny v teorii priblizheniya. M., 1984. [3] Miroshnichenko V.L. Reshenie kraevoy zadachi dlya differentsial'nogo uravneniya metodom splayn- funktsiy. Skhema povyshennoy tochnosti.// Izv. AN Kaz. SSR. Ser. Fizika-Matematika. 1973. № 3. S. 37–42. [4] Dronov S.G., Ligun A.A. Ob odnom splayn- metode resheniya kraevoy zadachi.// UMZh. !989. T. 41, № 5. S. 703 – 707. [5] Dronov S.G. O priblizhenii splaynami resheniya kraevoy zadachi.// Issledovaniya po sovremennym problemam summirovaniya i priblizheniya funktsiy i ikh prilozheniyam. Dnepropetrovsk: DGU. 1987. S. 30– 37. [6] Dronov S.G. Primenenie splaynov po neravnomernoy setke k priblizhennomu resheniyu kraevykh zadach.// Voprosy optimal'noy approksimatsii funktsiy i summirovaniya ryadov. Dnepropetrovsk: DGU. 1988. S. 26– 32. [7] Dronov S.G., Khudaya Zh.V. O splayn-skheme povyshennoy tochnosti resheniya zadachi Koshi.// Priblizhenie funktsiy i summirovanie ryadov. Dnepropetrovsk: DGU. 1992. S. 29–38. [8] Dronov S.G., Khudaya Zh.V. O splayn-skheme povyshennoy tochnosti resheniya zadachi Koshi dlya uravneniya s razryvnymi koeffitsientami.// Matematichne modelyuvannya. Dneprodzerzhisk: DGTU. 1994. № 1. S. 17–20. [9] Dronov S.G. Splayn-metod nablygenogo reshenija differencialnyh uravnenij s razryvnymi koeffitsientami// Matematichne modelyuvannya. Dneprodzerzhisk: DGTU. 2016. № 1. S. 42–44. [10] Dronov S.G., Tonkonog Е.А. Metod reshenija kraevoy zadachi s vykoristaniem kvaziinterpolachionyh splajnov //Voprosy prikladnoj matematiki і matematicnogo modelirovanija.– D. :DNU. –2014.– S. 303– 310. [11] Khudaya Zh.V., Tonkonog Е.А. Metod reshenija kraevoy zadachi so smeshanymi granichnymi uslovijami // Voprosy prikladnoj matematiki і matematicnogo modelirovanija.– D. :DNU. – 2015. S. 218– 225.
Authors and Affiliations
С. Г. Дронов
Keywords
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