A numerical-analytic method for three-point boundary-value problems

Ronto, N. I.; Savina, Tatiana

doi:10.1007/bf01060411

Cited by 5 publications

(2 citation statements)

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“…The boundary value problems with parameters both in the non-linear differential equations and in the linear boundary boundary conditions were investigated in [8], [9], [10], [11], [12], [13] by using the so called numerical-analytic method based upon successive approximations [8], [13].…”

Section: Introductionmentioning

confidence: 99%

On parametrized problems with non-linear boundary conditions

Rontó¹,

Shchobak²

2003

Proceedings of the 7'th Colloquium on the Qualitative Theory of Differential Equations (July 14--18, 2003, Szeged, Hungary) Edi

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We consider a parametrized boundary-value problem containing an unknown parameter both in the non-linear ordinary differential equations and in the non-linear boundary conditions. By using a suitable change of variables, we reduce the original problem to a family of those with linear boundary conditions plus some non-linear algebraic determining equations. We construct a numerical-analytic scheme suitable for studying the solutions of the transformed boundary-value problem. Acknowledgement 1. The first author was partially supported by the scholarship Charles Simonyi.

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Section: Introductionmentioning

confidence: 99%

On parametrized problems with non-linear boundary conditions

Rontó¹,

Shchobak²

2003

Proceedings of the 7'th Colloquium on the Qualitative Theory of Differential Equations (July 14--18, 2003, Szeged, Hungary) Edi

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“…Later, appropriate versions of this method were developed for handling more general types of nonlinear boundary value problems for ordinary and functional-differential equations. We refer, e.g., to the books [3][4][5], the articles [6][7][8][9][10][11][12], and the series of survey articles [13] for the related references.…”

Section: Introductionmentioning

confidence: 99%

Numerical-analytic technique for investigation of solutions of some nonlinear equations with Dirichlet conditions

2011

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The article deals with approximate solutions of a nonlinear ordinary differential equation with homogeneous Dirichlet boundary conditions. We provide a scheme of numerical-analytic method based upon successive approximations constructed in analytic form. We give sufficient conditions for the solvability of the problem and prove the uniform convergence of the approximations to the parameterized limit function. We provide a justification of the polynomial version of the method with several illustrating examples.

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Limit theorems in the theory of multipoint boundary-value problems

Teplinskii¹,

Nedokis²

1999

Ukr Math J

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A numerical-analytic method for three-point boundary-value problems

Cited by 5 publications

References 1 publication

On parametrized problems with non-linear boundary conditions

On parametrized problems with non-linear boundary conditions

Numerical-analytic technique for investigation of solutions of some nonlinear equations with Dirichlet conditions

Limit theorems in the theory of multipoint boundary-value problems

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