COMPARISON GE & AGE METHODES ON HYPERBOLICAL EQUATIONS (WAVE EQUATIONS)

Abstract

The main objective of this thesis is a study of the numerical solution of hyperbolical partial differential equations. Deals with a general description and classification of partial differential equations. Some useful mathematical preliminaries are outlined. By employing finite differences the differential system is replaced by a large matrix system. Important concepts such as convergence, consistency, stability and accuracy are discussed with some detail. By coupling existing difference equations to approximate the given Hyperbolic, we arrive at the set of explicit equations, the equations of the point to the right and left boundary. The GE schemes are Constructed along a similar line as their accuracies, stability and truncation error established. Based on the scheme a class of parallel Alternative group explicit (AGE) iterative methods is derived accuracy, stability and convergence analysis is given.