Error propagation of general linear methods for ordinary differential equations

被引：17

作者：

Butcher, J. C. ^{[2
]}

Jackiewicz, Z. ^{[3
]}

Wright, W. M. ^{[1
]}

机构：

[1] La Trobe Univ, Dept Math & Stat Sci, Melbourne, Vic 3086, Australia

[2] Univ Auckland, Dept Math, Auckland, New Zealand

[3] Arizona State Univ, Dept Math, Tempe, AZ 85287 USA

来源：

JOURNAL OF COMPLEXITY | 2007年 / 23卷 / 4-6期

基金：

美国国家科学基金会;

关键词：

general linear methods; Nordsieck representation; error propagation; local error estimation for methods of adjacent orders; adaptive stepsize selection; stability analysis;

D O I：

10.1016/j.jco.2007.01.009

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We discuss error propagation for general linear methods for ordinary differential equations up to terms of order p + 2, where p is the order of the method. These results are then applied to the estimation of local discretization errors for methods of order p and for the adjacent order p + 1. The results of numerical experiments confirm the reliability of these estimates. This research has applications in the design of robust stepsize and order changing strategies for algorithms based on general linear methods. (c) 2007 Published by Elsevier Inc.

引用

页码：560 / 580

页数：21

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