Estimating the Global Error of Runge-Kutta Approximations for Ordinary Differential Equations
The user of a code for solving the initial value problem for ordinary differential systems is normally left with the difficult task of assessing the accuracy of the numerical result returned by the code. Even when the code reports an estimate of the global error, the question may remain whether this estimate is correct, i. e. whether the user can rely on the estimate. This paper proposes a simple idea of measuring the reliability of the global error estimate with the aim of assisting the user in the validation of the numerical result. The idea is put into practice with the existing code GERK (ACM Algorithm 504) developed by Shampine and Watts. This code uses global Richardson extrapolation for the error estimation, which in many cases can also be applied to Runge-Kutta codes for delay equations.
KeywordsCoarse Grid Global Error Stiff Problem Parallel Integration Local Error Estimation
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