2017/02/10 by Mikel Antoñana, Antoñana, Mikel, Joseba Makazaga +3 · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1702.03354
openalex publication_date 2017/02/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We propose an implementation of symplectic implicit Runge-Kutta schemes for\nhighly accurate numerical integration of non-stiff Hamiltonian systems based on\nfixed point iteration. Provided that the computations are done in a given\nfloating point arithmetic, the precision of the results is limited by round-off\nerror propagation. We claim that our implementation with fixed point iteration\nis near-optimal with respect to round-off error propagation under the\nassumption that the function that evaluates the right-hand side of the\ndifferential equations is implemented with machine numbers (of the prescribed\nfloating point arithmetic) as input and output. In addition, we present a\nsimple procedure to estimate the round-off error propagation by means of a\nslightly less precise second numerical integration. Some numerical experiments\nare reported to illustrate the round-off error propagation properties of the\nproposed implementation.\n