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• W2016067905 endingPage "1845" @default.
• W2016067905 startingPage "1833" @default.
• W2016067905 abstract "The convergence of chaotic attractors is demonstrated for increasingly finer spatial discretizations of a dissipative partial differential equation using both the traditional and nonlinear Galerkin methods. This is done for the complex Ginzburg-Landau equation which describes amplitude evolution of instability waves in fluid flow. Density functions of instantaneous Lyapunov exponents are used to establish the convergence. These exponents measure the local variations in the contraction/expansion rates along an orbit. The results indicate that the convergence of the density functions requires no more iterations in time than is needed for convergence of the classical Lyapunov exponent. Thus the density function, which gives a more detailed description of the orbit, can serve as a viable means of comparing different methods of spatial discretization as well as the effect of finer resolution. The density function converged faster, i.e. with fewer modes, in the case of the nonlinear Galerkin method than in the traditional Galerkin method." @default.
• W2016067905 created "2016-06-24" @default.
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• W2016067905 creator A5074156162 @default.
• W2016067905 date "1995-10-01" @default.
• W2016067905 modified "2023-10-14" @default.
• W2016067905 title "Convergence of a chaotic attractor with increased spatial resolution of the Ginzburg-Landau equation" @default.
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• W2016067905 doi "https://doi.org/10.1016/0960-0779(94)00197-x" @default.
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