Accession Number : ADA124846


Title :   Accuracy of Finite Difference Methods for Solution of the Transient Heat Conduction (Diffusion) Equation.


Descriptive Note : Master's thesis,


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


Personal Author(s) : Chivers,Thomas Sidney , Jr


Full Text : http://www.dtic.mil/dtic/tr/fulltext/u2/a124846.pdf


Report Date : Feb 1983


Pagination or Media Count : 97


Abstract : The two-dimensional transient heat conduction (diffusion) equation was solved using the fully explicit, fully implicit, Crank-Nicholson implicit, and Peaceman-Rachford alternating direction implicit (ADI) finite difference methods (FDMTHs). The general stability condition for the same FDMTHs was derived by the matrix, coefficient, and a probabilistic method. The matrix, coefficient, and probabilistic methods were found to be equivalent in that each lead to the same general stability condition. Oscillatory behavior of the fully explicit FDMTH was as predicted by the general stability condition. Though the Crank-Nicholson implicit and the Peaceman-Rachford ADI FDMTHs were expected to be unconditionally stable, unstable oscillations were observed for large sizes of time step. For large numbers of time steps and sizes of time steps for which all FDMTHs considered are stable, the Crank-Nicholson implicit FDMTH is the more accurate. (Author)


Descriptors :   *FINITE DIFFERENCE THEORY , *THERMAL DIFFUSION , *THERMAL CONDUCTIVITY , *PARTIAL DIFFERENTIAL EQUATIONS , COMPUTER PROGRAMS , STABILITY , TWO DIMENSIONAL , COMPARISON , ACCURACY , THESES , SOLUTIONS(GENERAL) , BOUNDARY VALUE PROBLEMS , NUMERICAL METHODS AND PROCEDURES , OSCILLATION


Subject Categories : Numerical Mathematics
      Thermodynamics


Distribution Statement : APPROVED FOR PUBLIC RELEASE