2017/09/19 by Bilman, Deniz, Trogdon, Thomas
#65L06 #65M12 #65M22 #65P10 #Computational Physics (physics.comp-ph) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Pattern Formation and Solitons (nlin.PS)
paper · doi:10.48550/arxiv.1709.06659
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.