Abstract

Purpose

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.

Methods

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.

Results

Several illustrative examples are given to demonstrate the effectiveness of the present method.

Conclusions

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.

Keywords:

Iterative reproducing kernel method; Beam equation; Fourth-order boundary value problem; Nonlinear boundary conditions