Optimal Residuals and the Dahlquist Test Problem
arXiv:1805.1097612 citationsh-index: 33
Originality Synthesis-oriented
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For researchers in numerical analysis, this offers a new perspective on stiff problem solvers, but the approach is limited to a simple test problem.
The paper computes the optimal relative backward error for the Dahlquist test problem using one-step methods, providing new insight into stiff problem numerical solutions.
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.