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Algorithmic Realization of an Exact Three-Point Difference Scheme for the Sturm–Liouville Problem

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We develop a new algorithmic implementation of the exact three-point difference schemes on a nonuniform grid for the Sturm–Liouville problem. It is shown that, in order to find the coefficients of exact scheme for an arbitrary node of the grid, it is necessary to solve two auxiliary Cauchy problems for second-order linear ordinary differential equations: one problem on the interval [x j−1, x j] (forward) and one problem on the interval [x j , x j+1] (backward). We prove the theorem on the coefficient stability of the exact three-point difference scheme.

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References

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Authors and Affiliations

  1. Lviv Polytechnic National University, Lviv, Ukraine

    А. V. Kunynets

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

    M. V. Kutniv & N. V. Khomenko

  3. Rzeszow Technological University, Rzeszow, Poland

    M. V. Kutniv

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  1. А. V. Kunynets
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  2. M. V. Kutniv
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  3. N. V. Khomenko
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Correspondence to M. V. Kutniv.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 1, pp. 37–51, January–March, 2020.

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Kunynets, А.V., Kutniv, M.V. & Khomenko, N.V. Algorithmic Realization of an Exact Three-Point Difference Scheme for the Sturm–Liouville Problem. J Math Sci 270, 39–58 (2023). https://doi.org/10.1007/s10958-023-06331-2

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