Conservation of energy,momentum and actions in numerical discretizations of non-linear wave equations |
| |
Authors: | David Cohen Ernst Hairer Christian Lubich |
| |
Institution: | (1) Mathematisches Institut, University of Basel, 4051 Basel, Switzerland;(2) Dept. de Mathématiques, University of Geneva, 1211 Geneva 4, Switzerland;(3) Mathematisches Institut, University of Tübingen, 72076 Tübingen, Germany |
| |
Abstract: | For classes of symplectic and symmetric time-stepping methods— trigonometric integrators and the Störmer–Verlet or leapfrog method—applied to spectral semi-discretizations of semilinear wave equations in a weakly non-linear setting, it is shown that energy, momentum, and all harmonic actions are approximately preserved over long times. For the case of interest where the CFL number is not a small parameter, such results are outside the reach of standard backward error analysis. Here, they are instead obtained via a modulated Fourier expansion in time. |
| |
Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35L70 65M70 65M15 |
本文献已被 SpringerLink 等数据库收录! |
|