Galerkin methods for the Davey–Stewartson equations

Galerkin methods for the Davey–Stewartson equations In this paper, we propose two Galerkin methods to investigate the evolution of the Davey–Stewartson equations. The extrapolated Crank–Nicolson scheme and decoupled semi-implicit multistep scheme are employed to increase the order of the time discrete accuracy, which only requires the solutions of a linear system at each time step. Four numerical experiments are presented to illustrate the features of the proposed numerical methods, such as the optimal convergence order, the conservation variable and the application in rogue waves. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

Galerkin methods for the Davey–Stewartson equations

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier Inc.
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.044
Publisher site
See Article on Publisher Site

Abstract

In this paper, we propose two Galerkin methods to investigate the evolution of the Davey–Stewartson equations. The extrapolated Crank–Nicolson scheme and decoupled semi-implicit multistep scheme are employed to increase the order of the time discrete accuracy, which only requires the solutions of a linear system at each time step. Four numerical experiments are presented to illustrate the features of the proposed numerical methods, such as the optimal convergence order, the conservation variable and the application in rogue waves.

Journal

Applied Mathematics and ComputationElsevier

Published: Jul 1, 2018

References

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