Сплайн-метод наближеного розв’язку диференціальних рівнянь з розривними коефіцієнтами
Journal Title: Математичне моделювання - Year 2016, Vol 1, Issue 1
Abstract
A SPLINE METHOD FOR APPROXIMATE SOLUTION OF DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS COEFFICIENTS Dronov S.G. Abstract This study presents an algorithm for approximate solving of a marginal problem for the common secondorder 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 splaynfunktsiy. 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. Zhanlav T. O predstavlenii interpolyatsionnykh kubicheskikh splaynov cherez V-splayny// Metody splayn-funktsiy. Vychislitel'nye sistemy. Novosibirsk, 1981. Vyp. 37.
Authors and Affiliations
С. Г. Дронов
Keywords
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