Accession Number : ADA141091

Title :   Applications of the Variational Integral in Iterative Numerical Solutions to the Stationary Heat Equations.

Descriptive Note : Master's thesis,

Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING

Personal Author(s) : MacDonald,M L

PDF Url : ADA141091

Report Date : Mar 1984

Pagination or Media Count : 96

Abstract : Three stationary heat equations were solved using the finite-difference method. The resulting set of algebraic equations were solved using the Gauss-Seidel iterative technique. The temperatures at the nodal points were substituted into a numerical approximation of the variational integral. The variational integral approximation was used to determine when to stop the iterative process. The variational integral stopping criterion was compared to a stopping criterion that uses the displacement between iterations to approximate the error between the iterative solution and the exact solution. The variational integral was found to be less effective as a stopping criterion than the error estimate. The variational integral was examined as a method of determining whether the finite-difference technique or the finite-element technique gave a more accurate solution. It was found that the variational integral failed, in some cases, to predict the more accurate method. (Author)

Descriptors :   *Variational principles, *Integrals, *Numerical analysis, *Iterations, Finite difference theory, Finite element analysis, Approximation(Mathematics), Stationary, Boundary value problems, Partial differential equations, Theses

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE