Abstract
AbstractWe 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.
Funder
King Abdullah University of Science and Technology
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Reference82 articles.
1. Abgrall, R., Nordström, J., Öffner, P., Tokareva, S.: Analysis of the SBP-SAT stabilization for finite element methods part I: Linear problems. J. Sci. Comput. 85(2), 1–29 (2020). https://doi.org/10.1007/s10915-020-01349-z. arxiv:1912.08108 [math.NA]
2. Alefeld, G., Potra, F.A., Shi, Y.: Algorithm 748: Enclosing zeros of continuous functions. ACM Trans. Math. Softw. (TOMS) 21(3), 327–344 (1995). https://doi.org/10.1145/210089.210111
3. Álvarez, J., Durán, A.: Error propagation when approximating multi-solitons: The KdV equation as a case study. Applied Mathematics and Computation 217(4), 1522–1539 (2010). https://doi.org/10.1016/j.amc.2009.06.033
4. Álvarez, J., Durán, A.: On the preservation of invariants in the simulation of solitary waves in some nonlinear dispersive equations. Commun. Nonlinear Sci. Numer. Simul. 17(2), 637–649 (2012). https://doi.org/10.1016/j.cnsns.2011.06.019
5. Antonopoulos, D.C., Dougalis, V.A., Mitsotakis, D.E.: Initial-boundary-value problems for the Bona-Smith family of Boussinesq systems. Adv. Differ. Equations 14(1/2), 27–53 (2009)
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