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

Abstract

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.