A practical approach for the derivation of algebraically stable two-step Runge-Kutta methods

Abstract

We describe an algorithm, based on a new strategy recently proposed by Hewitt and Hill in the context of general linear methods, for the construction of algebraically stable two-step Runge-Kutta methods. Using this algorithm we obtained a complete characterization of algebraically stable methods with one and two stages.

Keywords

• ordinary differential equations
• two-step Runge-Kutta methods
• general linear methods
• G-stability
• algebraic stability