A-stable and Stiffly-stable Formulas in Generalized Linear Multistep Methods for Ordinary Differential Equations

摘要

In this paper, generalized linear multistep methods for ODEs whose predictor of off-grid point is an implicit formula are proposed and stability properties are investigated for the methods. Then, it is proved that there exists a family of A-stable methods of order 3 and, furthermore, there exists a unique A-stable one-step method of order 4. Also, it is numerically shown that there exist two families of stiffly stable methods, with orders 5 and 7, respectively.