Open Access Research

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

Andrei Rontó1, Miklos Rontó2, Gabriela Holubová3 and Petr Nečesal3*

Author Affiliations

1 Institute of Mathematics, Academy of Sciences of the Czech Republic, Brno, Czech Republic

2 Department of Analysis, University of Miskolc, Egyetemvaros, Hungary

3 Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

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Boundary Value Problems 2011, 2011:58 doi:10.1186/1687-2770-2011-58

Published: 28 December 2011

Abstract

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.

Keywords:
nonlinear boundary value problem; numerical-analytic method; Chebyshev interpolation polynomials