2013/08/16 by Janosch Rieger, Rieger, Janosch
Engineering · Mathematics · Physics and Astronomy · #34A60 #65L20 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1308.3643
openalex publication_date 2013/08/16 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
The Euler scheme is up to date the most important numerical method for\nordinary differential inclusions, because the use of the available higher-order\nmethods is prohibited by their enormous complexity after spatial\ndiscretization. Therefore, it makes sense to reassess the Euler scheme and\noptimize its performance. In the present paper, a considerable reduction of the\ncomputational cost is achieved by setting up a numerical method that computes\nthe boundaries instead of the complete reachable sets of the fully discretized\nEuler scheme from lower-dimensional data only. Rigorous proofs for the\npropriety of this method are given, and numerical examples illustrate the gain\nof computational efficiency as well as the robustness of the scheme against\nchanges of topology of the reachable sets.\n