# Optimal Time Step Control for the Numerical Solution of Ordinary Differential Equations

@inproceedings{Utumi1996OptimalTS,
title={Optimal Time Step Control for the Numerical Solution of Ordinary Differential Equations},
author={Masaki Utumi and Ryuji Takaki and Toshio Kawai},
year={1996}
}
In solving differential equations using a finite stepsize $h$, an error $Eh^{p+1}$ is generated at each step and propagates. This phenomenon is treated as a dynamical process, where $h(t)$ is controlled to optimize a properly defined performance index. Applying the variational principle, optimal stepsize is found to be proportional to $(E\psi)^{-\frac{1}{p+1}}$, where $E$ is the error generation coefficient and $\psi$ is the adjoint function of the error variable. This means that conventional… CONTINUE READING

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