Reciprocal Function Method for Cauchy Problems with First-Order Poles

For the numerical solution of the Cauchy problem with multiple poles, we propose a reciprocal function method. In the case of first-order poles, it makes it possible to continue the solution through the poles and to determine the solution and the pole positions with good accuracy. The method allows...

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Veröffentlicht in:Doklady. Mathematics 2020-03, Vol.101 (2), p.165-168
Hauptverfasser: Belov, A. A., Kalitkin, N. N.
Format: Artikel
Sprache:eng
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Zusammenfassung:For the numerical solution of the Cauchy problem with multiple poles, we propose a reciprocal function method. In the case of first-order poles, it makes it possible to continue the solution through the poles and to determine the solution and the pole positions with good accuracy. The method allows one to employ conventional explicit and implicit schemes, for example, explicit Runge–Kutta schemes. A test problem with multiple poles is computed as an example. The proposed method is useful for construction of software for direct computation of special functions.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562420020040