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Identifier

uch.math.phd//1995zouraris

Title

Ανάλυση αριθμητικών μεθόδων για δυναμικές μερικές διαφορικές εξισώσεις

Alternative Title

Analysis of numerical methods for dynamical partial differential equations

Creator

Zouraris, George

Abstract

We consider on initial and Neumann boundary value problem for a general parabolic aquation and an analogous one, with Dirichlet boundary conditions, for a Sobolev - Galpern type equation. We approximate the solution of these problems using a fully discrete scheme, which is based on the combination of a standard Galerkin finite element method with a Runge-Kutta method. Also, we prove a priori error estimates of fractional order, in L2 norm, for the parabolic equation and of optinal order, in several norms, for the Sobolev - Galpern equation. We also consider, a Schrodinger type equation in a non cylindrical domain under Dirichlet boundary conditions. We construct a family of conservative finite difference methods, which are based on proper approximations of the morning boundary. Finaly, we present on optimal order error estimate in a discrete L2 norm.

Issue date

1995-05-01

Date available

1997-06-6

Collection

School/Department--School of Sciences and Engineering--Department of Mathematics--Doctoral theses

Type of Work--Doctoral theses

Views

773

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