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A Fast Spectral Algorithm for Nonlinear Wave Equations with Linear Dispersion

✍ Scribed by Bengt Fornberg; Tobin A. Driscoll

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 264 KB
Volume: 155
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.1999.6351

No coin nor oath required. For personal study only.

✦ Synopsis

Spectral algorithms offer very high spatial resolution for a wide range of nonlinear wave equations on periodic domains, including well-known cases such as the Korteweg-de Vries and nonlinear Schrödinger equations. For the best computational efficiency, one needs also to use high-order methods in time while somehow bypassing the usual severe stability restrictions. We use linearly implicit multistep methods, with the innovation of choosing different methods for different ranges in Fourier space-high accuracy at low wavenumbers and A-stability at high wavenumbers. This new approach compares favorably to alternatives such as split-step and integrating factor (or linearly exact) methods.

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