Some efficient Nordsieck integration methods for IVPs

Abstract

In this paper, in continuation of the construction of efficient numerical methods for stiff IVPs, we construct type two Nordsieck second derivative general linear methods with order p = s, where s is the number of internal stages, and stage order q = p. Implementation of the constructed methods with fixed and variable stepsize is discussed which verifies their efficiency.

Keywords

• stiff differential equations
• nordsieck second derivative general linear methods
• a- and l-stability
• variable stepsize implementation