Power Series Methods II. The Heat Equation.
Abstract
The power series method is applied to the heat equation. Highly accurate semi-discrete systems of equations in t and in x are generated and are made stable by proper choice of parameters. A totally discrete scheme is produced that represents arbitrarily high accuracy in both x and t. Stability analysis indicates that while arbitrary order in t may be stable, the order of accuracy in x is restricted to be less than 16 and certain geometrical restrictions on the step sizes must be met. Truncation errors are examined and a consistency condition is obtained that further restricts the step sizes. The scheme is shown to coincide with Keller's Box scheme in its lowest order.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1979
- Accession Number
- ADA068940
Entities
People
- Robert D. Small
Organizations
- University of Wisconsin–Madison