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We compare performances of well-known numerical time-stepping methods thatare widely used to compute solutions of the doubly-infiniteFermi-Pasta-Ulam-Tsingou (FPUT) lattice equations. The methods are benchmarkedaccording to (1) their accuracy in capturing the soliton peaks and (2) incapturing highly-oscillatory parts of the solutions of the Toda latticeresulting from a variety of initial data. The numerical inverse scatteringtransform method is used to compute a reference solution with high accuracy. Wefind that benchmarking a numerical method on pure-soliton initial data can leadone to overestimate the accuracy of the method.

Benchmarking Numerical Methods for Lattice Equations with the Toda Lattice