In this chapter we discuss discrete variable methods for solving BVPs for ordinary differential equations. These methods produce solutions that are defined on a set of discrete points. Methods of this type are initial-value techniques, i.e., shooting and superposition, and finite difference schemes. We will discuss initialvalue and finite difference methods for linear and nonlinear BVPs, and th...

in this paper, we investigate the goursat problem in the class c21(d)cn0 (d  p) c00 (d q)for a third order pseudoparabolic equation. some results are given concerning the existence and uniquenessfor the solution of the suggested problem.

The Difference Potential Method (DPM) [1] proved to be a very efficient tool for solving boundary value problems (BVPs) in complex regions. It allows BVPs to be reduced to a boundary equation without the knowledge of Green’s functions. The method has been successfully used for solving very different problems related to the solution of partial differential equations [1]. However, it has mostly b...

The theory of time scales was introduced by Hilger in his Ph.D. thesis 1 in 1988 in order to unify continuous and discrete analysis. The study of dynamic equations on time scales is a fairly new subject and research in this area is rapidly growing. For some basic definitions and relevant results on time scales, see 2, 3 . Recently, first-order boundary value problems BVPs for short on time scal...

In this paper, a singularly perturbed system of reaction–diffusion Boundary Value Problems (BVPs) is examined. To solve such a type of problems, a Modified Initial Value Technique (MIVT) is proposed on an appropriate piecewise uniform Shishkin mesh. The MIVT is shown to be of second order convergent (up to a logarithmic factor). Numerical results are presented which are in agreement with the th...