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

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 solvabi...

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Bibliographic Details
Published in:Boundary value problems 2011-12, Vol.2011 (1), p.58-58, Article 58
Main Authors: Rontó, Andrei, Rontó, Miklos, Holubová, Gabriela, Nečesal, Petr
Format: Article
Language:English
Subjects:
Analysis
Approximations and Expansions
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary: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. 2000 Mathematics Subject Classification: 34B15; 65L10.
ISSN:1687-2770
1687-2770
DOI:10.1186/1687-2770-2011-58