Multistage optimal homotopy asymptotic method for solving boundary value problems with robin boundary conditions

In this paper, a new reliable algorithm called the multistage optimal homotopy asymptotic method (MOHAM) based on the standard optimal homotopy asymptotic method (OHAM) for solving secondorder nonlinear boundary value problems (BVPs) is presented. The new algorithm is a modification of the OHAM, in which it is based on partitioning the domain into two, or more, subdomains, where we compute a separate series in each subdomain using our new modified scheme for nonlinear BVPs. This modification provides us with a simple way to control the convergence of approximation series and adjust the convergence region when necessary and does not depend upon small or large parameters. Numerical comparison between the MOHAM results and the exact solution reveals that this method is a promising tool for solving second-order nonlinear BVPs.