Optimal Residuals and the Dahlquist Test Problem
Numerical Analysis
2018-05-29 v1
Abstract
We show how to compute the \emph{optimal relative backward error} for the numerical solution of the Dahlquist test problem by one-step methods. This is an example of a general approach that uses results from optimal control theory to compute optimal residuals, but elementary methods can also be used here because the problem is so simple. This analysis produces new insight into the numerical solution of stiff problems.
Cite
@article{arxiv.1805.10976,
title = {Optimal Residuals and the Dahlquist Test Problem},
author = {Robert M. Corless and C. Yalcin Kaya and Robert H. C. Moir},
journal= {arXiv preprint arXiv:1805.10976},
year = {2018}
}
Comments
23 figures (sized incorrectly for this arxiv version---see the worksheet at publish.uwo.ca/~rcorless/Dahlquist/ResidualAnalysis-3D-Contours.mw for better versions