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

被引：0
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作者：
Andrei Rontó
Miklos Rontó
Gabriela Holubová
Petr Nečesal
机构：
[1] Academy of Sciences of the Czech Republic,Institute of Mathematics
[2] University of Miskolc,Department of Analysis
[3] University of West Bohemia,Department of Mathematics
来源：
Boundary Value Problems | / 2011卷
关键词：
nonlinear boundary value problem; numerical-analytic method; Chebyshev interpolation polynomials;
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摘要：
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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