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

Fìz.-mat. model. ìnf. tehnol. 2021, 32:186-190

  • Andrii Kunynets Lviv Polytechnic National University
  • Myroslav Kutniv Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
  • Nadia Khomenko Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine
Keywords: Sturm-Liouville problem, exact three-point difference scheme, three-point difference schemes of high order of accuracy, iterative Newton method

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.

References
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Published
2021-07-08
How to Cite
Kunynets, A., Kutniv, M., & Khomenko, N. (2021). Solving the Sturm-Liouville problem by three-point difference schemes of high order of accuracy. PHYSICO-MATHEMATICAL MODELLING AND INFORMATIONAL TECHNOLOGIES, (32), 186-190. https://doi.org/10.15407/fmmit2021.32.186