A GENERAL-THEORY OF STABILIZED EXTENDED ONE-STEP METHODS FOR ODES

To overcome the ''order barrier'' imposed by A-stability on linear mul tistep methods (LMMs) several authors have constructed A-stabilized ex tended one-step methods of order m by coupling m-1 LLMs for 2 less tha n or equal to m less than or equal to 5. In the present paper we discu ss an alternative derivation technique for these methods based on Rung e-Kutta methods (RKM). With this technique we are able to present exam ples of A-stable and L-stable methods for 2 less than or equal to m le ss than or equal to 7.