Modification of Lesnic’s Approach and New Analytic Solutions for Some Nonlinear Second-Order Boundary Value Problems with Dirichlet Boundary Conditions

Abstract

For solving nonlinear boundary value problems (BVPs), a main difficulty of using Adomian’s method is to find a canonical form which takes into account all the boundary conditions of the problem. This difficulty is overcome by using a modification for Lesnic’s approach developed in this paper. The effectiveness of the proposed procedure is verified by two nonlinear problems: the nonlinear oscillator equation and Troesch’s problem