A new approach to error estimation for general linear methods for ODEs

Z. Jackiewicz, J.C. Butcher

Department of Mathematics & Statistics, Arizona State University, Tempe, Arizona 85287, USA

jackiewi@math.la.asu.edu

http://math.la.asu.edu/~jackiewi/zdzislaw.html

Contributed talk

We present a simple, accurate and reliable approach to the estimation of the local discretization error for general linear methods for ordinary differential equations. In this approach the input vector for the next step from $x_n$ to $x_{n+1}=x_n+h$ is rescaled and modified accordingly to compensate for the change of stepsize from $\bar{h}$ to $h=r\bar{h}$. The error estimates that have been obtained are very accurate and reliable for any stepsize pattern for both explicit and implicit methods. They are much more accurate than the error estimates derived previously in [1], where error estimates were evaluated numerically as the computation proceeds from step to step.