Realization of the exact three-point finite-difference schemes for the system of second-order ordinary differential equations

• Datum: 2023
• Hauptverfasser: Makarov, V. L., Mayko, N. V., Ryabichev, V. L., Макаров, В. Л., Майко, Н. В., Рябічев, В. Л.
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2023
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/7373
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.9 + 519.6 We consider the exact three-point finite-difference scheme (EDS) for the Dirichlet boundary-value problem for a system of second-order ODEs.  We find weaker conditions (as compared to the 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.  We show 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 a 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.