Abstract
The purpose of this study is the design of efficient methods for the solution of an ordinary differential system of equations arising from the semidiscretization of a hyperbolic partial differential equation. Jameson recently introduced the use of one-step Runge-Kutta methods for the numerical solution of the Euler equations. Improvements in efficiency up to 80% may be achieved by using two-step Runge-Kutta methods instead of the classical onestep methods. These two-step Runge-Kutta methods were first introduced by Byrne and Lambert in 1966. They are designed to have the same number of function evaluations as the equivalent one-step schemes, and thus they are potentially more efficient. By solving a nonlinear programming problem, which is specified by stability requirements, optimal two-step schemes are designed. The optimization technique is applicable for stability regions of any shape.
Original language | English (US) |
---|---|
Pages (from-to) | 563-579 |
Number of pages | 17 |
Journal | Mathematics of Computation |
Volume | 55 |
Issue number | 192 |
DOIs | |
State | Published - 1990 |
Keywords
- Hyperbolic partial differential equations
- Method of lines
- Pseudo-Runge-Kutta methods
- Stability
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics