Publications in Scientific Journals:
W. Auzinger, O. Koch:
"An improved local error estimator for symmetric time-stepping schemes";
Applied Mathematics Letters,
We propose a symmetrized version of the defect to be used in the estimation of the local time-stepping error of symmetric one-step methods for the time propagation of linear autonomous evolution equations. Using the anti-commutator of the numerical flow and the right-hand side operator in the definition of the defect of the numerical approximation, a local error estimator is obtained which has higher accuracy asymptotically than an established version using the common defect. This theoretical result is illustrated for a splitting method applied to a linear Schrödinger equation.
numerical time integration, one-step methods, symmetric schemes, local error estimation
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