Solution of Higher-Order, Multipoint, Nonlinear Boundary Value Problems with High-Order Robin-Type Boundary Conditions by the Adomian Decomposition Method

In this paper, we propose a new modified recursion scheme for the approximate solution of higher-order, multipoint, nonlinear boundary value problems with higher-order Robin-type boundary conditions by the Adomian decomposition method. Our new approach utilizes all of the boundary conditions to derive an equivalent nonlinear Fredholm-Volterra integral equation before establishing the new modified recursion scheme for the solution. We solve several complex numerical examples obtaining a rapidly convergent sequence of analytic functions as the solution. In all cases investigated, we achieved an approximately exponential rate of convergence, thus confirming that only a few terms of the Adomian decomposition series can provide an accurate engineering model for parametric simulations.