Benchmarking numerical methods for lattice equations with the Toda lattice


We compare the performance 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.

Applied Numerical Mathematics 141, 19–35, 2019
Deniz Bilman
Deniz Bilman
Assistant Professor

Assistant Professor of Mathematics.