A New Method for Solving the Cauchy Problem for Systems of Ordinary Differential Equations

Oleg N. Lytvyn; Lyudmila S.  Lobanova; Galina A. Miroshnychenko

doi:10.1615/JAutomatInfScien.v46.i9.10

Journal of Automation and Information Sciences

Главный редактор: Arkadiy A. Chikriy (open in a new tab)

Ассоциированный редакторs: Vyacheslav F. Gubarev (open in a new tab) Yuriy P. Kondratenko (open in a new tab) Nonna V. Turovyerova (open in a new tab)

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ISSN Печать: 1064-2315

ISSN Онлайн: 2163-9337

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A New Method for Solving the Cauchy Problem for Systems of Ordinary Differential Equations

Том 46, Выпуск 9, 2014, pp. 1-11

DOI: 10.1615/JAutomatInfScien.v46.i9.10

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Oleg N. Lytvyn
Ukrainian Engineering and Pedagogical Academy, Kharkov

Lyudmila S. Lobanova
Ukrainian Engineering and Pedagogical Academy, Kharkov

Galina A. Miroshnychenko
Ukrainian Engineering and Pedagogical Academy, Kharkov

Краткое описание

A new method for finding an approximate solution of the Cauchy problem for systems of linear ordinary differential equations is proposed. The approximate solution is represented as a linear combination of the elements of a system of linearly independent functions. The unknown constants of expansion into a series are found from the condition of the best approximation of the right-hand sides of the differential equations of the system (by the norm L₂ [0, 1]) and their derivatives (by the norm W₂ [0, 1]), using the indicated system of linearly independent functions. Examples are given.

Ключевые слова: systems of linear ordinary differential equations, Cauchy problem, approximate analytical solution, splines technique, optimization

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