Existence and Numerical Method for Nonlinear Third-Order Boundary Value Problem in the Reproducing Kernel Space
1 Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China
2 School of Mathematics and Sciences, Harbin Normal University, Harbin, Heilongjiang 150025, China
Boundary Value Problems 2010, 2010:459754 doi:10.1155/2010/459754Published: 2 February 2010
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.