
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 WRIGHTPATTERSON 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 finitedifference method. The resulting set of algebraic equations were solved using the GaussSeidel 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 finitedifference technique or the finiteelement 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