Date of Award:

5-1982

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee Chair(s)

Chris Coray

Committee

Chris Coray

Committee

Lawrence Cannon

Committee

Russell Thompson

Committee

Ian Anderson

Abstract

This paper surveys reasons why the Ritz method and the Galerkin method are not efficient and why these methods can not be applied directly, for time dependent problems. It also introduces methods that are used for those problems. For a linear boundary value problem defined by a positive definite symmetric (self-adjoint) operator, the existence and the convergence of the Ritz approximation are guaranteed. In non-symmetric case, Lax-Milgram lemma assures the existence and the convergence of the Galerkin approximation for H1/2(Ω)-elliptic operator. Since time dependent problems are hyperbolic or parabolic, the existence and the convergence of approximations by those methods are not guaranteed. Moreover, those methods were originally developed for boundary value problems. Thus new techniques are introduced in order to extend those methods to initial-boundary value problems.

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