Asymptotic (h→∞) Absolute Stability for BDFs Applied to Stiff Differential Equations

Abstract

Methods based on backward differentiation formulas (BDFs) for solving stiff differential equations require iteratmg to approximate the solution of the corrector equation on each step. One hope for reducmg the cost of this is to make do with iteration matrices that are known to have errors and to do no more iterations than are necessary to mamtam the stability of the method. This paper, following work by Klopfenstem, examines the effect of errors m the iteration matrix on the stability of the method. Application of the results to an algorithm IS discussed briefly. © 1984, ACM. All rights reserved.