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.

On the parametrization of three-point nonlinear boundary-value problems

We analyze the application of the numerical-analytic method proposed by A.M. Samoilenko in 1965 to multipoint boundary-value problems.

The theory of the numerical-analytic method: Achievements and new trends of development. VI

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.

Modification of the numerical-analytical method of successive approximations for boundary-value problems in ordinary differential equations

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. We also obtain several existence results for problems with deviations of an argument.

Application of the Numerical-Analytic Method to Systems of Differential Equations with Parameter

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. Implicit systems of the neutral type with deviated arguments are also considered.

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Numerical-analytic method for implicit differential equations

Numerical-analytic method for solving boundary-value problems for ordinary differential equations

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A. M. Samoilenko

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Numerical-analytic method for solving boundary-value problems for ordinary differential equations