2019/11/29 by Harald Hofstätter, Hofstätter, Harald, Winfried Auzinger +3
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #FOS: Mathematics #Modeling and Simulation Systems #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1912.01399
openalex publication_date 2019/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper discusses an efficient implementation of the generation of order\nconditions for the construction of exponential integrators like exponential\nsplitting and Magnus-type methods in the computer algebra system Maple. At the\ncore of this implementation is a new algorithm for the computation of\ncoefficients of words in the formal expansion of the local error of the\nintegrator. The underlying theoretical background including an analysis of the\nstructure of the local error is briefly reviewed. As an application the\ncoefficients of all 8th order self-adjoint commutator-free Magnus-type\nintegrators involving the minimum number of 8 exponentials are computed.\n