Article ID Journal Published Year Pages File Type
5776091 Journal of Computational and Applied Mathematics 2017 12 Pages PDF
Abstract
In the process of studying the conjecture, Colliander, Keel, Staffilani, Takaoka, and Tao introduced a “toy model” dynamical system as an approximation of NLS, which has been subsequently studied numerically. In this work, we formulate and examine several numerical schemes for integrating this model equation. The model has two invariants, and our schemes aim to conserve at least one of them. We prove convergence in some cases, and our numerical studies show that the schemes compare favorably to others, such as Trapezoidal Rule and fixed step fourth order Runge-Kutta. The preservation of the invariants is particularly important in the study of weak turbulence as the energy transfer tends to occur on long time scales.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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