High-order generalized-$\alpha$ methods
Numerical Analysis
2019-02-15 v1
Abstract
The generalized- method encompasses a wide range of time integrators. The method possesses high-frequency dissipation while minimizing unwanted low-frequency dissipation and the numerical dissipation can be controlled by the user. The method is unconditionally stable and is of second-order accuracy in time. We extend the second-order generalized- method to third-order in time while the numerical dissipation can be controlled in a similar fashion. We establish that the third-order method is unconditionally stable. We discuss a possible path to the generalization to higher order schemes. All these high-order schemes can be easily implemented into programs that already contain the second-order generalized- method.
Cite
@article{arxiv.1902.05253,
title = {High-order generalized-$\alpha$ methods},
author = {Quanling Deng and Pouria Behnoudfar and Victor M. Calo},
journal= {arXiv preprint arXiv:1902.05253},
year = {2019}
}