Journal Article10.1007/BF01099232
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
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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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Abstract: 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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Citations
Some remarks on an integral equation arising in applications of numerical-analytic method of solving of boundary value problems
TL;DR: In this paper, the comparison method and the choosing of the appropriate norm of the comparison operator are used to establish the solvability of the integral functional equation as a result of the application of the numerical-analytic method of solving of boundary value problems for ordinary differential-delay equations of the neutral type.
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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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Justification of a numerical-analytic method of successive approximations for problems with integral boundary conditions
A. M. Samoilenko,S. V. Martynyuk +1 more
TL;DR: In this paper, a numerical-analytic method of successive approximations to investigation and approximate construction of solutions of differential equations with integral boundary conditions is presented for application of a numerical analytic method.
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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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Modified Projection-Iterative Method for Weakly Nonlinear Integrodifferential Equations with Parameters
TL;DR: In this paper, a modified projection-iterative method is used to solve boundary value problems for weakly nonlinear integrodifferential equations with parameters, and the authors substantiate the application of the modified projection iterative method to the solution of boundary-value problems.
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