Boundary Value Problems
Volume 2010 (2010), Article ID 459754, 19 pages
doi:10.1155/2010/459754

Existence and numerical method for nonlinear third-order boundary value problem in the reproducing kernel space

Abstract

We are concerned with general third-order nonlinear boundary value problems. An existence theorem of solution is given under weaker conditions. In the meantime, an iterative algorithm with global convergence is presented. The higher order derivatives of approximate solution is obtained by using this method can approximate the corresponding derivatives of exact solution well.