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):

Report Date:

1984-03-01

Pagination or Media Count:

96.0

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

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE