Global Error Estimates for Ordinary Differential Equations
- 1 June 1976
- journal article
- Published by Association for Computing Machinery (ACM) in ACM Transactions on Mathematical Software
- Vol. 2 (2) , 172-186
- https://doi.org/10.1145/355681.355687
Abstract
The user of a code for solving the initial value problem for ordinary differential equations is normally interested in the global error, i.e. the difference between the solution of the problem posed and the numerical result returned by the code. This paper describes a way of estimating the global error reliably while still solving the problem with acceptable efficiency. Global extrapolation procedures are applied to parallel solutions obtained by a Runge-Kutta-Fehlberg method. These ideas are implemented in a Fortran program called GERK, which is ACM Algomthm 504.Keywords
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