A general theory of stabilized extended one-step methods for odes

Abstract

To overcome the “order barrier” imposed by A-stability on linear multistep methods (LMMs) several authors have constructed A-stabilized extended one-step methods of order m by coupling m−1 LLMs for 2 ≤ m ≤ 5. In the present paper we discuss an alternative derivation technique for these methods based on Runge-Kutta methods (RKM). With this technique we are able to present examples of A-stable and L-stable methods for 2 ≤ m ≤ 7.

Keywords:

• Initial-value problems
• ODEs
• Extended one-step methods
• A-stability
• L-stability

C.R.Categories:

• G.1.7
• G.1.0

^∗ Research director at the National Fund for Scientific Research (N.F.W.O. Belgium).

^∗ Research director at the National Fund for Scientific Research (N.F.W.O. Belgium).

Notes

^∗ Research director at the National Fund for Scientific Research (N.F.W.O. Belgium).