Journal Article10.1007/BF02592043
The theory of the numerical-analytic method: Achievements and new trends of development. VI
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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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Abstract: We analyze the application of the numerical-analytic method proposed by A.M. Samoilenko in 1965 to multipoint boundary-value problems.
read more
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Citations
Successive Approximation Techniques in Non-Linear Boundary Value Problems for Ordinary Differential Equations
András Rontó,Miklós Rontó +1 more
- 01 Jan 2008
TL;DR: In this paper, the solvability and the approximate construction of solutions of regular non-linear boundary value problems for systems of ODEs on a compact interval were investigated, where the value of the parameter introduced artificially into the scheme is to be determined by solving a certain system of algebraic or transcendental equations.
41
On a cauchy-nicoletti type three-point boundary value problem for linear differential equations with argument deviations
András Rontó,Miklós Rontó +1 more
TL;DR: In this paper, it is shown that it is useful to reduce the problem to the parametrized two-point boundary value problem for a suitably perturbed system containing some artificially introduced parameters both in the constructed inhomogeneous twopoint boundary conditions and in the modified functional differential equations.
On Nonseparated Three-Point Boundary Value Problems for Linear Functional Differential Equations
András Rontó,Miklós Rontó +1 more
TL;DR: In this article, a parametric family of two-point boundary value problems for a suitably perturbed linear functional differential system is studied. But the authors consider a three-point problem with nonseparated boundary conditions determined by singular matrices.
Succesive approximation method for some linear boundary value problems for differential equations with a special type of argument deviation
András Rontó,Miklós Rontó +1 more
TL;DR: In this article, successive approximation techniques for the investigation of solutions of some linear two-point boundary value problems for differential equations with special types of argument deviation are discussed, and the authors discuss successive approximation algorithms for solving these problems.
13
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.
12
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