An unconventional finite difference technique for the solution of two-point third-order boundary value problems in ODEs

Abstract

In this article, the boundary value problem involving third order differential equations in ODEs in a close open domain is considered and boundary conditions prescribed at the two points. A non conventional finite difference method developed for the approximate numerical solution of the problem. Our proposed technique is simple in application and solves the problem directly and uses boundary conditions in a natural way. We have established the quadratic order of accuracy and convergence of the proposed method analytically. The numerical results in computational experiments on model test problem both nonlinear and linear, verify the competency and established order of the convergence of the proposed method. Also a singular problem considered and satisfying numerical results obtained in computational experiments as an extended application of the method.