Optimization-Based Search for Nordsieck Methods of High Order with Quadratic Stability Polynomials

Abstract

We describe the search for explicit general linear methods in Nordsieck form for which the stability function has only two nonzero roots. This search is based on state-of-the-art optimization software. Examples of methods found in this way are given for order p = 5, p = 6, and p = 7.

Keywords:

• general linear methods
• Nordsieck methods
• quadratic stability
• least-squares minimization

AMS Subject Classification:

• 65L05
• 65L20
• 65K05