Solving the Sturm-Liouville problem by three-point difference schemes of high order of accuracy-Reference-Cited by-同舟云学术

Solving the Sturm-Liouville problem by three-point difference schemes of high order of accuracy

Published:2021-07-08 Issue:32 Volume: Page:186-190
ISSN:1816-1545
Container-title:Physico-mathematical modelling and informational technologies
language:
Short-container-title:Fìz.-mat. model. ìnf. tehnol.

Author:

Kunynets Andrii¹,Kutniv Myroslav²,Khomenko Nadia²

Affiliation:

1. Lviv Polytechnic National University

2. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine

Abstract

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.

Publisher

National Academy of Sciences of Ukraine (Co. LTD Ukrinformnauka)

Reference6 articles.

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3. Prikazchikov, V. G. (1969). “High-accuracy homogeneous difference schemes for the Sturm-Liouville problem,” Zh. Vychisl. Mat. Mat. Fiz., 9(2), 315–336. https://doi.org/10.1016/0041-5553(69)90095-0.

4. 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. https://doi.org/10.1007/978-3-0348-0107-2.

5. 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).