Third-order BVPs: Fixed-point iteration scheme

Abstract

A new approachis introduced for the solution of a wide class of third order linear and nonlinear boundary value problems (BVPs). The method is based on embedding Green’s functions into well-established fixed point iterations, including Picard’s and Krasnoselskii-Mann’s schemes. The effectiveness of the proposed method is established by implementing it on several numerical examples, including linear and nonlinear third order BVPs. The resulting numerical solutions are compared with both the analytical and the numerical solutions that exist in the literature.