Abstract
We suggest a modification of A. M. Samoilenko's numerical-analytic method for investigating the problemdx/dt=f(t,x),
{here,
is a linear continuous operator} in which it is not necessary to solve an additional determining equation.
References
A. M. Samoilenko and N. I. Ronto,Numerical-Analytic Methods in the Theory of Boundary-Value Problems for Ordinary Differential Equations [in Russian], Naukova Dumka, Kiev (1992).
E. P. Trofimchuk, “Integral operators of the method of successive periodic approximations,”Mat. Fiz. Nelin. Mekh., Issue 13 (47), 31–36 (1990).
E. P. Trofimchuk,Iterative Methods for Investigation of Differential Systems with Singularities [in Russian], Author's Abstract of the Candidate Degree Thesis (Physics and Mathematics), Kiev (1992).
E. P. Trofimchuk, “On the improvement of convergence estimates in a numerical-analytic method for a problem with integral conditions,” in:Analytic Methods for Investigation of Nonlinear Differential Systems, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 115–119.
A. M. Samoilenko and N. I. Ronto,Numerical-Analytic Methods for Investigation of Solutions of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1986).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 138–140, January, 1995.
This research was partially supported by the Ukrainian State Committee on Science and Technology.
Rights and permissions
About this article
Cite this article
Trofimchuk, E.P., Kovalenko, A.V. A. M. Samoilenko's numerical-analytic method without determining equation. Ukr Math J 47, 163–166 (1995). https://doi.org/10.1007/BF01058810
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01058810