An improved local error estimator for symmetric time-stepping schemes

作者：Auzinger Winfried; Koch Othmar

来源：Applied Mathematics Letters, 2018, 82: 106-110.

DOI：10.1016/j.aml.2018.03.001

• Numerical time integration
• One-step methods
• Symmetric schemes
• Local error estimation

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 Schrodinger equation.

• 出版日期2018-8