Stabilizing Averages for Multistep Methods of Solving Ordinary Differential Equations

摘要

In 1959 Milne and Reynolds described a technique of 'stabilizing averages' for damping out the increasingly disruptive oscillations of the error associated with certain multistep methods for solving ordinary differential equations numerically. In 1965 Timlake published a constructive proof of the fact that stabilizing averages exist for all conditionally stable multistep methods and in particular, he proved the existence of stabilizing averages for Milne's method which reduce by a factor of theeta(h superscript(2k+1)) the disruptive component of the truncation error expression for any non-negative integer k. Numerical experiments were carried out to verify Timlake's theoretical results and the results are presented in this report. (Author)