Power Series Methods III. The Wave Equation.
Abstract
The power series method used to generate highly accurate finite difference schemes for ordinary differential equations is here applied to the wave equation. The analysis involves semi-discrete approximations in t and in x before the totally discrete scheme is derived. The results differ in that an arbitrarily accurate difference scheme is found for the wave equation that is stable and consistent with the differential equation. No such scheme exists for the heat equation. The step sizes in x and t must be equal for this difference scheme. Other difference schemes that do not restrict the step sizes are stable only when the order of accuracy in x is less than 5. The lowest order scheme is shown to coincide with Keller's Box Scheme.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1979
- Accession Number
- ADA068941
Entities
People
- Robert D. Small
Organizations
- University of Wisconsin–Madison