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Realization of the Exact Three-Point Finite-Difference Schemes for the System of Second-Order Ordinary Differential Equations

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Ukrainian Mathematical Journal Aims and scope

We consider an exact three-point finite-difference scheme (EDS) for the Dirichlet boundary-value problem for a system of second-order ordinary differential equations with boundary conditions of the first kind. We find weaker (as compared with known) conditions under which the analyzed scheme can be represented in the divergence form. The coefficient stability of the EDS and the accuracy of the perturbed scheme are investigated. It is shown that the matrix coefficients and the right-hand side of the equation can be represented via the solutions of four initial-value problems on the intervals whose length is equal to the length of grid step. The solutions of these problems can be obtained by using an arbitrary one-step method, which leads to a truncated difference scheme of a certain rank.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    V. L. Makarov

  2. T. Shevchenko Kyiv National University, Kyiv, Ukraine

    N. V. Mayko & V. L. Ryabichev

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  1. V. L. Makarov
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  2. N. V. Mayko
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  3. V. L. Ryabichev
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Correspondence to N. V. Mayko.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, No. 1, pp. 72–95, January, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i1.7373.

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Makarov, V.L., Mayko, N.V. & Ryabichev, V.L. Realization of the Exact Three-Point Finite-Difference Schemes for the System of Second-Order Ordinary Differential Equations. Ukr Math J 75, 80–106 (2023). https://doi.org/10.1007/s11253-023-02187-6

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  • DOI: https://doi.org/10.1007/s11253-023-02187-6

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