DOI
https://doi.org/10.25772/WAV4-6029
Defense Date
1981
Document Type
Thesis
Degree Name
Master of Science
Department
Mathematical Sciences
First Advisor
Jerrold S. Rosenbaum
Abstract
In order to obtain a numerical solution to the heat equation using finite differences, either implicit or explicit equations are used to formulate a solution. The advantage in an explicit formulation is its simplicity and minimal computer storage requirements while its disadvantage is its instability. The opposite is true for an implicit formulation such as the Crank-Nicolson method; although it is stable it is more difficult to implement and requires a much larger memory capacity. In this paper we examine the accuracy and stability of a hybrid approach, a modified Crank-Nicolson formulation, that combines the advantageous features of both the implicit and explicit formulations. This hybrid approach results in a 20% reduction in the amount of work required compared to the standard Crank-Nicolson solution if both methods use a special tridiagonal system solver. If Gaussian elimination is used, the modified Crank-Nicolson approach reduces the amount of work by 87%. Regardless of the linear system solver used, the modified Crank-Nicolson approach reduces by 50% the memory requirement of the standard Crank-Nicolson method.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
10-30-2017
Comments
Scanned, with permission from the author, from the original print version, which resides in University Archives.