Explicit Runge-Kutta methods for the numerical solution of initial value problems

Charalampos Tsitouras

Explicit Runge-Kutta methods for the numerical solution of initial value problems

Authors

Charalampos Tsitouras Department of Applied Mathematics and Physical Sciences, National Technical University of Athens, Zografou Campus 15780, Athens, Greece.

Keywords:

order conditions, truncation error, stability, embedded pairs, phase-lag

Abstract

Explicit Runge-Kutta pairs are the most popular methods for integrating non-stiff initial value problems. Basic theory concerning its occuracy, stability and other properties is presented here as long as with implementation issues. Finally a new pair of orders 5(4) suitable for oscillatory problems is presented and tested.