An approximate solution for the static beam problem and nonlinear integro-differential equations

We consider a Kirchhoff type nonlinear static beam and an integro-differential convolution type problem, and investigate the effectiveness of the Optimal Homotopy Asymptotic Method (OHAM), in solving nonlinear integro-differential equations. We compare our solutions via the OHAM, with bench mark solutions obtained via a finite element method, to show the accuracy and effectiveness of the OHAM in each of these problems. We show that our solutions are accurate and the OHAM is a stable accurate method for the problems considered.