A-stable and L-stable block implicit one-step methods with modified algorithm

摘要

A class of A-stable and L-stable block implicit one-step methods were studied in Zhou [9]. If the nodes within block were reasonablely chosen, it was shown that the methods had several attractive properties. Here we give a quick review of the methods. Then we discuss the error estimate and step control policy. A C program, ABIOS_4, is given at end of the paper which uses modified algorithm suggested in [9].