A novel fixed point iteration method for the solution of third order boundary value problems

In this work, a new alternative uniformly convergent iterative scheme is presented and applied for the solution of an extended class of linear and nonlinear third order boundary value problems that arise in physical applications. The method is based on embedding Green’s functions into well-known fixed point iterations, including Picard’s and Krasnoselskii–Mann’s schemes. Convergence of the numerical method is proved by manipulating the contraction principle. The effectiveness of the proposed approach is established by implementing it on several numerical examples, including linear and nonlinear third order boundary value problems. The results show highly accurate approximations when compared to exact and existing numerical solutions.