Iterative method for solving a nonlinear boundary value problem

In this paper, a boundary value problem for a nonlinear second-order ordinary differential equation is studied. By means of the maximum principle we established the existence and the uniqueness of a solution of the problem. Then for finding the solution an iterative method is proposed. It is proved that this method converges much faster than the Picar successive approximations and in a particular case it gives two-sided monotone approximations to the exact solution of the problem. Finally, some illustrative examples are considered to confirm the efficiency of the method. Ó 2007 Elsevier Inc. All rights reserved.

• Type: Journal
• Year: 2007
• Where: AMC
• Authors: A. Dang Quang
• Keywords: AMC 2007, Boundary Value Problem, Ordinary Differential Equation, Picar Successive Approximations