Instability and local truncation error estimate in runge-kutta type methods

Abstract

The interaction of instability and local truncation error estimate for the general explicit Runge-Kutta method of order p is discussed. It is proved that this estimate indicates the presence of instability when the above method is applied to the numerical solution of the initial value problem. It is also shown why a test designed to monitor the local truncation error estimate does in fact also monitor the stability of the integration.

Keywords:

• Initial value problem
• truncation error estimate
• absolute stability
• Runge-Kutta methods
• step control algorithm

C.R. Categories:

• G.1.7 Single step methods