Numerical solution of Cauchy problems with multiple poles of integer order

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Abstract

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.

About the authors

Aleksandr A. Belov

Lomonosov Moscow State University; Peoples’ Friendship University of Russia (RUDN University)

Email: aa.belov@physics.msu.ru
ORCID iD: 0000-0002-0918-9263

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

1, bld. 2, Leninskie Gory, Moscow, 119991, Russian Federation; 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Nikolay N. Kalitkin

Keldysh Institute of Applied Mathematics RAS

Author for correspondence.
Email: kalitkin@imamod.ru
ORCID iD: 0000-0002-0861-1792

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

4A, Miusskaia Sq., Moscow, 125047, Russian Federation

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