By C. Cercignani (auth.), Renato Spigler (eds.)
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Additional info for Applied and Industrial Mathematics: Venice - 1, 1989
D. dissertation, University of California, Berkeley. 48 c. W. , Ruehli, A. , and Sangiovanni-Vincent elli , A. , "The waveform relaxation method for time-domain analysis of large scale integrated circuits", IEEE Trans. on CAD of IC and Sys. Vol. 3, pp. 131-145, July 1982. , "Remarks on Picard-Lindelof iteration", REPORT-MAT-A254, Helsinki University of Technology, Institute of Mathematics, Finland, December 1987.  Wells, D. , "Multirate linear multistep methods for the solution of systems of ordinary differential equations", Report No.
Symplectic schemes for Hamiltonian systems do not imply non-Hamiltonian perturbations, but they do inevitably imply Hamiltonian perturbations. An example is the break-down of invariant tori when the scheme is applied to integrable or near integrable systems. The effect is indiscernible for small step size, but becomes pronounced with large step sizes, see Fig 5. Another example is the artificial chaos in the form of Arnold diffusion. We computed by explicit symplectic schemes (21) of order 2, the Hamiltonian system Hie (22) with k-fold rotational symmetry in 1 degree of freedom, suggested by Sagdeev, Zaslavsky et al [18J in the context of chaotic stream lines of Lagrangian turbulence, see also [19-21J.
FI. (I at I at 111. 6. Hamiltonian with 4-fold rotational symmetry, using Hk in (22), k = 4. Explicit symplectic composite scheme, order 2 (21). , total number of steps=N , number of steps per plot =M. 2, N=40,000, M=1. In the symplectic scheme for system with Hamiltonian Hk , the initial point, chosen on or very near to a separatrix, moves within an Arnold web which is a network of canals with the separatrices as its skeleton. The canals become thinner with smaller,... The separatrix network of H4 is a square lattice.
Applied and Industrial Mathematics: Venice - 1, 1989 by C. Cercignani (auth.), Renato Spigler (eds.)