Computations related to G-stability of linear multistep methods

[摘要] In Dahlquist's recent proof of the equivalence of A-stability and G-stability, an algorithm was presented for calculating a G-stability matrix for any A-stable linear multistep method. Such matrices, and various quantities computable from them, are useful in many aspects of the study of the stability of a given method. For example, information may be gained as to the shape of the stability region, or the rate of growth of unstable solutions. We present a summary of the relevant theory and the results of some numerical calculations performed for several backward differentiation, Adams-Bashforth, and Adams-Moulton methods of low order.

[学科分类] 计算机科学（综合）