Journal Article10.1007/BF01085735
Numerical-analytic method for solving boundary-value problems for ordinary differential equations
A. M. Samoilenko,V. A. Ronto +1 more
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About: This article is published in Ukrainian Mathematical Journal. The article was published on 01 Jan 1982. The article focuses on the topics: Numerical partial differential equations & Exponential integrator.
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Citations
On the parametrization of three-point nonlinear boundary-value problems
TL;DR: In this paper, a three-point boundary value problem for a system of nonlinear differential equations is reduced to a family of two-point problems, whose solutions are investigated by using the numerical-analytic method.
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The theory of the numerical-analytic method: Achievements and new trends of development. VI
TL;DR: In this article, the application of the numerical-analytic method proposed by A.M. Samoilenko in 1965 to multipoint boundary value problems is analyzed, and the results show that the numerical analysis can be used to solve the problem.
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Modification of the numerical-analytical method of successive approximations for boundary-value problems in ordinary differential equations
A. M. Samoilenko,N. I. Ronto +1 more
TL;DR: In this paper, a method to improve convergence of successive approximations in the study of existence and in the constructin of approximate solutions of nonlinear differential equations in the case of periodic and linear two-point boundary conditions is presented.
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Application of the Numerical-Analytic Method to Systems of Differential Equations with Parameter
TL;DR: In this paper, the numerical analytic method is applied to systems of differential equations with parameter under the assumption that the corresponding functions satisfy the Lipschitz conditions in matrix notation, and several existence results for problems with deviations of an argument are obtained.
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Numerical-analytic method for implicit differential equations
TL;DR: In this paper, the numerical analytic method combined with the comparison one based on suc- cessive approximations is used to investigate solutions of implicit differential equations with integral boundary conditions. But this method does not consider implicit systems of the neutral type with deviated arguments.