A computational method for nonlinear 2m‐th order boundary value problems

Abstract

In this paper, two point boundary value problems of 2mth‐order nonlinear differential equations are considered. The existence of the solution and a new iterative algorithm which is large‐range convergent are proposed for the problems in reproducing kernel space. The advantage of the approach must lie in the fact that, on the one hand, for the arbitrary fixed initial value function, the iterative method is convergent. On the other hand, the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives, respectively. Some examples are displayed to demonstrate the computation efficiency of the method.

Foundation item: Supported by National Natural Science Foundation of China (No. 60572125); Heilongjiang Institute of Science and Technology (No. 07–17); Heilongjiang province education department science and technology (No. 11531324).

First published online: 10 Feb 2011

Keyword : boundary value problems, nonlinear differential equation, existence, reproducing kernel space