Picard iteration-based variable-order integrator with dense output employing algorithmic differentiation
| Autor: | Bela Erdelyi, Afnan Al Marzouk, Herman D. Schaumburg |
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| Rok vydání: | 2018 |
| Předmět: |
Automatic differentiation
Applied Mathematics Numerical analysis 010103 numerical & computational mathematics 01 natural sciences Machine epsilon Numerical integration 010101 applied mathematics Variable (computer science) Fixed-point iteration Integrator Theory of computation 0101 mathematics Algorithm Mathematics |
| Zdroj: | Numerical Algorithms. 80:377-396 |
| ISSN: | 1572-9265 1017-1398 |
| DOI: | 10.1007/s11075-018-0489-z |
| Popis: | Motivated by the high accuracy requirements and the huge ratio of the largest to smallest time scales of Coulomb collision simulations of a considerable number of charges, we developed a novel numerical integration scheme, which uses algorithmic differentiation to produce variable, high-order integrators with dense output. We show that Picard iterations are not only a nice theoretical tool, but can also be successfully implemented to develop competitive integrators, especially when accuracies close to machine precision are required. The numerical integrators’ performance and applications to the electrostatic n-body problem are illustrated. |
| Databáze: | OpenAIRE |
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