GLOBAL ERROR ESTIMATION WITH RUNGE-KUTTA METHODS

被引：27

作者：

DORMAND, JR

DUCKERS, RR

PRINCE, PJ

机构：

[1] TEESSIDE POLYTECH,DEPT MATH & STAT,MIDDLESBROUGH TS1 3BA,CLEVELAND,ENGLAND

[2] TEESSIDE POLYTECH,DEPT COMP SCI,MIDDLESBROUGH TS1 3BA,CLEVELAND,ENGLAND

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 1984年 / 4卷 / 02期

关键词：

Errors - Numerical methods - Ordinary differential equations - Runge Kutta methods;

D O I：

10.1093/imanum/4.2.169

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An analysis of global error estimation for Runge - Kutta solutions of ordinary differential equations is presented. The basic technique is that of Zadunaisky in which the global error is computed from a numerical solution of a neighbouring problem related to the main problem by some method of interpolation. It is shown that Runge - Kutta formulae which permit valid global error estimation using low-degree interpolation can be developed, thus leading to more accurate and computationally convenient algorithms than was hitherto expected. Some special Runge - Kutta processes up to order 4 are presented together with numerical results. © 1984, by Academic Press Inc. (London) Limited.

引用

页码：169 / 184

页数：16