Type-Insensitive ODE Codes Based on Implicit A( alpha ): Stable Formulas

摘要

This paper is a sequel to the paper which treats A-stable formulas. Although largely independent, it cannot be properly understood without the companion paper. For this reason and to avoid repetition of some lengthy arguments, it is presumed that the reader has studied that paper. Many of the most popular formulas for the solution of stiff ODE problems are not A-stable so that extending the analysis of the first paper is of great practical value. The backward differentiation formulas (BDF) of orders 3 to 6 are examples which are A( alpha )-stable, and may be thought of as prototypes for the formulas treated here. (ERA citation 06:019608)