A new high accuracy method in exponential form based on off-step discretization for non-linear two point boundary value problems

摘要

This paper is intended to describe a graded mesh implicit method based upon half step discretization of order three for the solution of non-linear two point boundary value problem of the form u'' = f (x, u, u'), x ∈ (a, b). The devised method is compact and uses three nodal points for the unknown function u(x) and two nodal points for the known variable 'x' in spatial axis. A detailed convergence analysis has also been included. This method, though meant for scalar equations was further extended to compute the vector equations of two point nonlinear boundary value problems. The method is directly applicable to singular problems. Computational results are provided to assess the performance and reliability of the method.