Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)3094910.22363/2658-4670-2022-30-2-105-114ArticlesСтатьиResearch ArticleNumerical solution of Cauchy problems with multiple poles of integer orderЧисленное решение задач Коши со множественными полюсами целого порядкаhttps://orcid.org/0000-0002-0918-9263BelovAleksandr A.БеловА. А.

Candidate of Physical and Mathematical Sciences, Associate Professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia (RUDN University); Researcher of Faculty of Physics, Lomonosov Moscow State University

aa.belov@physics.msu.ruhttps://orcid.org/0000-0002-0861-1792KalitkinNikolay N.КалиткинН. Н.

Doctor of Physical and Mathematical Sciences, Professor, Corresponding member of the RAS, head of department

kalitkin@imamod.ruLomonosov Moscow State UniversityМосковский государственный университет им. М.В. ЛомоносоваPeoples’ Friendship University of Russia (RUDN University)Российский университет дружбы народовKeldysh Institute of Applied Mathematics RASИнститут прикладной математики им. М.В. Келдыша РАН03052022302VOL 30, NO2 (2022)ТОМ 30, №2 (2022)10511403052022Copyright ©; 2022, Belov A.A., Kalitkin N.N.Copyright ©; 2022, Белов А.А., Калиткин Н.Н.2022Belov A.A., Kalitkin N.N.Белов А.А., Калиткин Н.Н.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/miph/article/view/30949

We consider Cauchy problem for ordinary differential equation with solution possessing a sequence of multiple poles. We propose the generalized reciprocal function method. It reduces calculation of a multiple pole to retrieval of a simple zero of accordingly chosen function. Advantages of this approach are illustrated by numerical examples. We propose two representative test problems which constitute interest for verification of other numerical methods for problems with poles.

Рассмотрена задачи Коши для обыкновенного дифференциального уравнения с решением, обладающим последовательностью кратных полюсов целого порядка. Предложен обобщённый метод обратной функции, который сводит вычисление кратного полюса к расчёту простого нуля соответственно выбранной функции. Преимущества такого подхода проиллюстрированы на численных примерах. Предложены сложные тестовые задачи, которые представляют интерес для проверки других численных методов для задач с полюсами.

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