CONSTRUCTION ОNE-STEP NINE POINTS BLOCK METHOD FOR SOLVING STIFF SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS

Tursunov D.A, Semenov M.E

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Research is devoted to the development of the theory of numerical methods in terms of constructing a linear implicit n-step k-points block methods for solving stiff systems of ordinary differential equations (ODEs). The example of the one-step linear implicit nine points block method in the form of backward differentiation formulas was written. Coefficients of the presented method were defined with the collocation technique. The conditions for consistency coefficients, the region of stability, the error constants, the convergence and the order accuracy of the method were defined. Numerical experiments of solving ODEs had been carried out with a MatLAB program. The proposed method is the self-starting method and it can be applied for the numerical solution of the Cauchy problem for the first order ODEs as well as system, including for stiff ones. The calculation of the approximate value of the unknown function for each k-th point in a block not depends from each other and it can be considered as a separate task.

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Турсунов Д.А, Семенов М.Е ПОСТРОЕНИЕ ОДНОШАГОВОГО ДЕВЯТИТОЧЕЧНОГО БЛОЧНОГО МЕТОДА ДЛЯ РЕШЕНИЯ ЖЕСТКИХ СИСТЕМ ОБЫКНОВЕННЫХ ДИФФЕРЕНЦИАЛЬНЫХ УРАВНЕНИЙ // Научное обозрение. Физико-математические науки . 2020. № 1. С. 58-58;
URL: https://physics-mathematics.ru/en/article/view?id=82 (дата обращения: 24.06.2026).