Direct integrators of modified multistep method for the solution of third order boundary value problem in ordinary differential equations

Abstract In this paper, we propose an efficient modified multistep method for direct solution of boundary value problems (BVPs) using multistep collocation approach. The continuous form was evaluated at grid and off-grid points to obtain the multiple finite difference schemes. The basic properties, such as order and error constants, zero stability and convergence analysis of the proposed methods were investigated. Numerical experiment were performed to show the efficiency of the method and the results were compared with the existing methods in the literature.