Efficient General Linear Methods of High Order with Inherent Quadratic Stability

Abstract

We search for general linear methods with s internal stages and r = s + 1 external stages of order p = s + 1 and stage order q = s. We require that stability function of these methods has only two non-zero roots. This is achieved by imposing the so-called inherent quadratic stability conditions. Examples of such general linear methods which are A- and L-stable up to the order p = 8 and stage order q = p - 1 are derived.

Keywords:

• general linear methods
• order and stage order
• A- and L-stability
• inherent quadratic stability

AMS Subject Classification:

• 65L05
• 65L20