On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations

Hendrik Ranocha (), Manuel Quezada Luna and David I. Ketcheson
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Hendrik Ranocha: University of Münster
Manuel Quezada Luna: King Abdullah University of Science and Technology (KAUST)
David I. Ketcheson: King Abdullah University of Science and Technology (KAUST)

Partial Differential Equations and Applications, 2021, vol. 2, issue 6, 1-26

Abstract: Abstract We study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of particular equations indicate that the error grows quadratically in time for numerical methods that do not conserve energy, but grows only linearly for conservative methods. We provide numerical experiments suggesting that this result extends to a very broad class of equations and numerical methods.

Keywords: Invariant conservation; Summation by parts; Spectral collocation methods; Relaxation schemes; Error growth rate; 65M12; 65M70; 65M06; 65M60; 65M20; 35Q35 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00126-3

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