Second derivative General Linear Method in Nordsieck form

Abstract

This paper considers the construction of second derivative general linear methods (SD-GLM) from hybrid LMM and their transformation to Nordsieck GLM. How the Runge-Kutta starters for the methods can be derived are given. The representation of the methods in Nordsieck form has the advantage of easy implementation in variable stepsize.

Keywords

• General linear methods (GLM)
• Nordsieck vectors/methods
• second derivative GLM
• RK-starters
• variable stepsize