Abstract
In this paper, we propose a numerical method to solve the boundary value problem involving third-order differential equations in ODEs in a closed--open domain, where the boundary conditions are prescribed at the closed and open end points. An application of interpolation and the smooth function method to incorporate the boundary condition at the open end point implied an unconventional finite difference method for the approximate numerical solution of the problem. Hence, the proposed method uses the boundary conditions in an exact and natural way. The method is simple in application and solves the problem directly. We have established the quadratic order of the accuracy and convergence of the proposed method analytically. The numerical results of computational experiments on model test problems, both nonlinear and linear, confirm the competency and the theoretical discussion on the order of convergence of the method. A singular problem is considered, and satisfying numerical results obtained in computational experiments is an extended application of the method.