Papers › An artificially-damped Fourier method for dispersive evolution equations
An artificially-damped Fourier method for dispersive evolution equations
Anne Liu, Thomas Trogdon
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Computing solutions to partial differential equations using the fast Fourier transform can lead to unwanted oscillatory behavior. Due to the periodic nature of the discrete Fourier transform, waves that leave the computational domain on one side reappear on the other and for dispersive equations these are typically high-velocity, high-frequency waves. However, the fast Fourier transform is a very efficient numerical tool and it is important to find a way to damp these oscillations so that this transform can still be used. In this paper, we accurately model solutions to four nonlinear partial differential equations on an infinite domain by considering a finite interval and implementing two damping methods outside of that interval: one that solves the heat equation and one that simulates rapid exponential decay. Heat equation-based damping is best suited for small-amplitude, high-frequency oscillations while exponential decay is used to damp traveling waves and high-amplitude oscillations. We demonstrate significant improvements in the runtime of well-studied numerical methods when adding in the damping method.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections