A New treatment of the finite difference method for 2-Interval Sturm-Liouville problems

Abstract

Ordinary and/or partial differential equations which satisfy certain initial and/or boundary conditions are appears in modeling of different kind of physical processes. To understand the nature of such physical processes it is needed to solve these initial and boundary value problems. But not all of these problems have exact analytical solution or it is impossible to find exact solution under realistic conditions.In most cases, may appear such types of differential equations that have exact solutions in terms of elementary functions that are difficult to obtain or is unhelpful to use. There are developed different type semi-analytical or approximation methods, such as the differential transform method, Runge-Kutta method, finite difference method, shooting method, homopoty perturbation method, Galerkin method, Adomian decomposition method, variational iteration method, weight resudial method and so on (\cite{asch}, \cite{atkins}, \cite{bur},