Algorithmic implementation of an exact three-point difference scheme for a certain class of singular Sturm–Liouville problems
| dc.citation.epage | 357 | |
| dc.citation.issue | 11 | |
| dc.citation.journalTitle | Математичне моделювання та комп'ютинг | |
| dc.citation.spage | 344 | |
| dc.citation.volume | 1 | |
| dc.contributor.affiliation | Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України | |
| dc.contributor.affiliation | Трірський університет | |
| dc.contributor.affiliation | Жешувський технологічний університет | |
| dc.contributor.affiliation | Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of the National Academy of Sciences of Ukraine | |
| dc.contributor.affiliation | Trier University | |
| dc.contributor.affiliation | Rzeszow University of Technology | |
| dc.contributor.author | Хоменко, Н. В. | |
| dc.contributor.author | Кутнів, М. В. | |
| dc.contributor.author | Khomenko, N. V. | |
| dc.contributor.author | Kutniv, M. V. | |
| dc.coverage.placename | Львів | |
| dc.coverage.placename | Lviv | |
| dc.date.accessioned | 2025-10-20T07:44:24Z | |
| dc.date.created | 2024-02-24 | |
| dc.date.issued | 2024-02-24 | |
| dc.description.abstract | У цій статті розроблено нову нову алгоритмічну реалізацію точних триточкових різницевих схем для певного класу сингулярних задач Штурма-Ліувілля. Ми демонструємо, що обчислення коефіцієнтів точної схеми в будь-якому вузлі сіткихй вимагає розв'язання двох допоміжних задач Коші для лінійних звичайних диференціальних рівнянь другого порядку: однієї задачі на інтервалі[хj − 1,хй] (вперед) та одна задача на інтервалі[хй,хj + 1] (назад). Доведено теорему про стійкість коефіцієнтів для точної триточкової різницевої схеми. | |
| dc.description.abstract | In this article, we present a new algorithmic implementation of exact three-point difference schemes for a certain class of singular Sturm–Liouville problems. We demonstrate that computing the coefficients of the exact scheme at any grid node xj requires solving two auxiliary Cauchy problems for the second-order linear ordinary differential equations: one problem on the interval [xj−1,xj] (forward) and one problem on the interval [xj,xj+1] (backward). We have also proven the coefficient stability theorem for the exact three-point difference scheme. | |
| dc.format.extent | 344-357 | |
| dc.format.pages | 14 | |
| dc.identifier.citation | Khomenko N. V. Algorithmic implementation of an exact three-point difference scheme for a certain class of singular Sturm–Liouville problems / N. V. Khomenko, M. V. Kutniv // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 344–357. | |
| dc.identifier.citationen | Khomenko N. V. Algorithmic implementation of an exact three-point difference scheme for a certain class of singular Sturm–Liouville problems / N. V. Khomenko, M. V. Kutniv // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2024. — Vol 1. — No 11. — P. 344–357. | |
| dc.identifier.doi | 10.23939/mmc2024.01.344 | |
| dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/113794 | |
| dc.language.iso | en | |
| dc.publisher | Видавництво Львівської політехніки | |
| dc.publisher | Lviv Politechnic Publishing House | |
| dc.relation.ispartof | Математичне моделювання та комп'ютинг, 11 (1), 2024 | |
| dc.relation.ispartof | Mathematical Modeling and Computing, 11 (1), 2024 | |
| dc.relation.references | [1] Tikhonov A. N., Samarskii A. A. Homogeneous difference schemes. USSR Computational Mathematics and Mathematical Physics. 1 (1), 5–67 (1962). | |
| dc.relation.references | [2] Tikhonov A. N., Samarskii A. A. Homogeneous difference schemes of a high degree of accuracy on nonuniform nets. USSR Computational Mathematics and Mathematical Physics. 1 (3), 465–486 (1962). | |
| dc.relation.references | [3] Prikazchikov V. G. High-accuracy homogeneous difference schemes for the Sturm–Liouville problem. USSR Computational Mathematics and Mathematical Physics. 9 (2), 76–106 (1969). | |
| dc.relation.references | [4] Makarov V. L., Gavrilyuk I. P., Luzhnykh V. M. Exact and truncated difference schemes for a class of degenerate Sturm–Liouville problems. Differentsial’nye Uravneniya. 16 (7), 1265–1275 (1980). | |
| dc.relation.references | [5] Gavrilyuk I. P., Hermann M., Makarov V. L., Kutniv M. V. Exact and truncated difference schemes for boundary value ODEs. International Series of Numerical Mathematics. 159. Birkh¨auser Basel (2011). | |
| dc.relation.references | [6] Kunynets A. V., Kutniv M. V., Khomenko N. V. Algorithmic realization of an exact three-point difference scheme for the Sturm–Liouville problem. Journal of Mathematical Sciences. 270 (1), 39–58 (2023). | |
| dc.relation.references | [7] Kunynets A. V., Kutniv M. V., Khomenko N. V. Three-point difference schemes of high accuracy order for Sturm–Liouville problem. Mathematical Methods and Physicomechanical Fields. 63 (4), 54–62 (2020). | |
| dc.relation.references | [8] Samarskii A. A., Makarov V. L. On the realization of exact three-point difference schemes for second-order ordinary differential equations with piecewise smooth coefficients. Soviet Mathematics. Doklady. 41 (3), 463–467 (1990). | |
| dc.relation.references | [9] Samarskii A. A., Makarov V. L. Realization of exact three-point difference schemes for second-order ordinary differential equations with piecewise smooth coefficients. Differ. Equat. 26 (7), 922–930 (1991). | |
| dc.relation.references | [10] Samarskii A. A. Introduction to the Theory of Difference Schemes. Nauka, Moscow (1971). | |
| dc.relation.references | [11] Hartman Ph. Ordinary differential equations. John Wiley & Sons, New York (1964). | |
| dc.relation.referencesen | [1] Tikhonov A. N., Samarskii A. A. Homogeneous difference schemes. USSR Computational Mathematics and Mathematical Physics. 1 (1), 5–67 (1962). | |
| dc.relation.referencesen | [2] Tikhonov A. N., Samarskii A. A. Homogeneous difference schemes of a high degree of accuracy on nonuniform nets. USSR Computational Mathematics and Mathematical Physics. 1 (3), 465–486 (1962). | |
| dc.relation.referencesen | [3] Prikazchikov V. G. High-accuracy homogeneous difference schemes for the Sturm–Liouville problem. USSR Computational Mathematics and Mathematical Physics. 9 (2), 76–106 (1969). | |
| dc.relation.referencesen | [4] Makarov V. L., Gavrilyuk I. P., Luzhnykh V. M. Exact and truncated difference schemes for a class of degenerate Sturm–Liouville problems. Differentsial’nye Uravneniya. 16 (7), 1265–1275 (1980). | |
| dc.relation.referencesen | [5] Gavrilyuk I. P., Hermann M., Makarov V. L., Kutniv M. V. Exact and truncated difference schemes for boundary value ODEs. International Series of Numerical Mathematics. 159. Birkh¨auser Basel (2011). | |
| dc.relation.referencesen | [6] Kunynets A. V., Kutniv M. V., Khomenko N. V. Algorithmic realization of an exact three-point difference scheme for the Sturm–Liouville problem. Journal of Mathematical Sciences. 270 (1), 39–58 (2023). | |
| dc.relation.referencesen | [7] Kunynets A. V., Kutniv M. V., Khomenko N. V. Three-point difference schemes of high accuracy order for Sturm–Liouville problem. Mathematical Methods and Physicomechanical Fields. 63 (4), 54–62 (2020). | |
| dc.relation.referencesen | [8] Samarskii A. A., Makarov V. L. On the realization of exact three-point difference schemes for second-order ordinary differential equations with piecewise smooth coefficients. Soviet Mathematics. Doklady. 41 (3), 463–467 (1990). | |
| dc.relation.referencesen | [9] Samarskii A. A., Makarov V. L. Realization of exact three-point difference schemes for second-order ordinary differential equations with piecewise smooth coefficients. Differ. Equat. 26 (7), 922–930 (1991). | |
| dc.relation.referencesen | [10] Samarskii A. A. Introduction to the Theory of Difference Schemes. Nauka, Moscow (1971). | |
| dc.relation.referencesen | [11] Hartman Ph. Ordinary differential equations. John Wiley & Sons, New York (1964). | |
| dc.rights.holder | © Національний університет “Львівська політехніка”, 2024 | |
| dc.subject | сингулярна задача Штурма–Ліувілля | |
| dc.subject | точна триточкова різницева схема | |
| dc.subject | коефіцієнтна стійкість | |
| dc.subject | singular Sturm–Liouville problem | |
| dc.subject | exact three-point difference scheme | |
| dc.subject | coefficient stability | |
| dc.title | Algorithmic implementation of an exact three-point difference scheme for a certain class of singular Sturm–Liouville problems | |
| dc.title.alternative | Алгоритмічна реалізація точної триточкової різницевої схеми для деякого класу сингулярних задач Штурма–Ліувілля | |
| dc.type | Article |
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