Iterative reproducing kernel method for a beam equation with third-order nonlinear boundary conditions
Department of Mathematics, Changshu Institute of Technology, 215500, People’s Republic of China
Mathematical Sciences 2012, 6:1 doi:10.1186/2251-7456-6-1Published: 18 May 2012
This paper investigates an analytical approximate solution of a fourth-order differential equation with nonlinear boundary conditions modeling beams on elastic foundations using iterative reproducing kernel method.
The solution obtained using the method takes the form of a convergent series with easily computable components. However, the reproducing kernel method can not be used directly to solve the problems since there is no method of obtaining a reproducing kernel satisfying nonlinear boundary conditions. The aim of this paper is to fill this gap.
Several illustrative examples are given to demonstrate the effectiveness of the present method.
Results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for the beam equation with third-order nonlinear boundary conditions.