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KIAM Preprint № 76, Moscow, 2020
Authors: Belov A.A., Kalitkin N.N.
Numerical integration of Cauchy problems with singularity points
Abstract:
We propose an effective method for solving Cauchy problem for an ordinary differential equation with multiple poles of an integer order. The method provides through calculation of a pole for both single pole and chain of poles. The method uses a special algorithm for finding the multiplicity of each pole. This multiplicity is used to define the generalized reciprocal function for which the K-th order pole of the initial function is a prime zero. Calculating such a zero is not difficult, so the proposed method provides high accuracy even near the poles. After passing this zero, the calculation of the initial function resumes. Using this method on a sequence of poles permits to find a numerical solution simultaneously with a posteriori estimation of its error. The method is illustrated with test examples.
Keywords:
Cauchy problem, singularities, continuation through pole
Publication language: russian,  pages: 36
Research direction:
Mathematical modelling in actual problems of science and technics
Russian source text:
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About authors:
  • Belov Alexander Alexandrovich,  ,  Faculty of Physics M.V. Lomonosov MSU; PFUR
  • Kalitkin Nikolaj Nikolaevich,  orcid.org/0000-0002-0861-1792KIAM RAS