Korotchenko, A. G.; Lapin, A. V. On an algorithm of numerical integration with the optimal choice of step. (Russian. English summary) Zbl 1037.65071 Vestn. Nizhegorod. Univ. N. I. Lobachevskogo, Mat. Model. Optim. Upr. 2001, No. 2, 270-278 (2001). A numerical integration algorithm for a class of systems of linear ordinary differential equations with the use of a simple difference scheme is considered. The integration steps are chosen so that the number of calculations of the right-hand part of the system is minimised and conditions for the precision are satisfied. Results of a numerical experiment are also given. Reviewer: V. I. Pinchukov (Novosibirsk) Cited in 1 Document MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L12 Finite difference and finite volume methods for ordinary differential equations 65L70 Error bounds for numerical methods for ordinary differential equations 34A30 Linear ordinary differential equations and systems Keywords:Cauchy problem; error bound; algorithm; systems; difference scheme; numerical experiment PDFBibTeX XMLCite \textit{A. G. Korotchenko} and \textit{A. V. Lapin}, Vestn. Nizhegorod. Univ. N. I. Lobachevskogo, Mat. Model. Optim. Upr. 2001, No. 2, 270--278 (2001; Zbl 1037.65071)