Important Aspects of Geometric Numerical Integration
Journal of Scientific Computing
New methods for oscillatory systems based on ARKN methods
Applied Numerical Mathematics
Geometric numerical integration by means of exponentially-fitted methods
Applied Numerical Mathematics
A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales
Journal of Computational Physics
Journal of Computational Physics
Stability of asynchronous variational integrators
Journal of Computational Physics
Error propagation in numerical approximations near relative equilibria
Journal of Computational and Applied Mathematics
Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations
Journal of Computational Physics
Efficient energy-preserving integrators for oscillatory Hamiltonian systems
Journal of Computational Physics
Exponential integrators for stiff elastodynamic problems
ACM Transactions on Graphics (TOG)
Error analysis of explicit TSERKN methods for highly oscillatory systems
Numerical Algorithms
Hi-index | 0.03 |
We consider second-order differential systems where high-frequency oscillations are generated by a linear part. We present a frequency expansion of the solution, and we discuss two invariants of the system that determine the coefficients of the frequency expansion. These invariants are related to the total energy and the oscillatory harmonic energy of the original system.For the numerical solution we study a class of symmetric methods that discretize the linear part without error. We are interested in the case where the product of the step size with the highest frequency can be large. In the sense of backward error analysis we represent the numerical solution by a frequency expansion where the coefficients are the solution of a modified system. This allows us to prove the near-conservation of the total and the oscillatory energy over very long time intervals.