Розв’язування задачі Штурма-Ліувілля триточковими різницевими схемами високого порядку точності: Fìz.-mat. model. ìnf. tehnol. 2021, 32:186-190

• Date: 2021
• Main Authors: Kunynets, Andrii, Kutniv, Myroslav, Khomenko, Nadia
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: задача Штурма-Ліувілля; точна триточкова різницева схема; триточкова рiзницева схема довільного порядку точності; ітераційний метод Ньютона
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/184
• Journal Title: Physico-mathematical modeling and informational technologies

For the solving Sturm-Liouville problem, three-point difference schemes of high order of accuracy on a nonuniform grid are constructed. It is shown that the coefficients of these schemes are expressed in terms of solutions of two auxiliary initial value problems. An estimate of the accuracy of three-point difference schemes is obtained and an iterative Newton method is proposed to determine their solution. Numerical experiments confirm theoretical conclusions. References Samarskii, A. A. (1971). Introduction to the Theory of Difference Schemes [in Russian], Nauka, Moscow. Makarov, V. L., Gavrilyuk, I. P., Luzhnykh, V. M. (1980). “Exact and truncated difference schemes for one class of Sturm–Liouville problems with degeneration,” Differents. Uravn., 16(7), 1265–1275. (in Russian). Prikazchikov, V. G. (1969). “High-accuracy homogeneous difference schemes for the Sturm-Liouville problem,” Zh. Vychisl. Mat. Mat. Fiz., 9(2), 315–336. DOI doi.org/10.1016/0041-5553(69)90095-0 Gavrilyuk, I. P., Hermann, M., Makarov, V. L., Kutniv, M. V. (2010). Exact and Truncated Difference Schemes for Boundary Value ODEs, Int. Series of Numer. Math. Birkhäuser, Springer, 159. DOI doi.org/10.1007/978-3-0348-0107-2 Kunynets, A. V., Kutniv, M.V., Khomenko, N.V. (2020). “Algoritmic realization of exact three-point difference scheme for Sturm – Liouville problem,” Mat. Met. Fiz.-Mekh. Polya, 63(1), 37–51. (in Ukrainian). Pryce, J. (1993). Numerical Solution of Sturm–Liouville Problems. –Oxford University Press, Oxford.