Benchmarking Numerical Methods for Lattice Equations with the Toda Lattice
Numerical Analysis
2017-09-29 v2 Pattern Formation and Solitons
Exactly Solvable and Integrable Systems
Computational Physics
Abstract
We compare performances of well-known numerical time-stepping methods that are widely used to compute solutions of the doubly-infinite Fermi-Pasta-Ulam-Tsingou (FPUT) lattice equations. The methods are benchmarked according to (1) their accuracy in capturing the soliton peaks and (2) in capturing highly-oscillatory parts of the solutions of the Toda lattice resulting from a variety of initial data. The numerical inverse scattering transform method is used to compute a reference solution with high accuracy. We find that benchmarking a numerical method on pure-soliton initial data can lead one to overestimate the accuracy of the method.
Cite
@article{arxiv.1709.06659,
title = {Benchmarking Numerical Methods for Lattice Equations with the Toda Lattice},
author = {Deniz Bilman and Thomas Trogdon},
journal= {arXiv preprint arXiv:1709.06659},
year = {2017}
}
Comments
21 pages, 30 figures, data tables in the appendix. A duplicate data table in Appendix B was replaced