Abstract
Solutions of many applied Cauchy problems for ordinary differential equations have one or more multiple zeros on the integration segment. Examples are the equations of special functions of mathematical physics. The presence of multiples of zeros significantly complicates the numerical calculation, since such problems are ill-conditioned. Round-off errors may corrupt all decimal digits of the solution. Therefore, multiple zeros should be treated as special points of the differential equations. In the present paper, a local solution transformation is proposed, which converts the multiple zero into a simple one. The calculation of the latter is not difficult. This makes it possible to dramatically improve the accuracy and reliability of the calculation. Illustrative examples have been carried out, which confirm the advantages of the proposed method.
Publisher
Peoples' Friendship University of Russia
Subject
Industrial and Manufacturing Engineering,Environmental Engineering
Reference15 articles.
1. E. Janke, F. Emde, and F. Losch, Tafeln Horer Functionen. Stutgart: B.G. Teubner Verlagsgesellschaft, 1960.
2. NIST Digital Library of Mathematical Functions, https://dlmf.nist.gov.
3. Studies on the zeros of Bessel functions and methods for their computation
4. N. N. Kalitkin and P. V. Koryakin, Numerical methods. Vol.2: Methods of mathematical physics [Chislennye Metody. T.2: Metody matematicheskoi fiziki]. Moscow: Akademiya, 2013, in Russian.
5. Numerical detection and study of singularities in solutions of differential equations