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Geometric pseudospectral method for spatial integration of dynamical systems. (English) Zbl 1225.37080

The authors suggest a spatial discretization scheme that preserves both the geometric structure of the port-Hamiltonian model, that is, the Dirac structure, and approximates the behaviour of the actual system in terms of conservation of energy and other conserved quantities. This means that in the lossless case some approximated extensive variables will be conserved (as a first integral) and that, in general, the dissipated power will be approximated conveniently. Finite difference schemes are often used by specialists in application domains but very specific formulations, and they seldom lead to general formulations with such desired geometric and energetic properties.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010)
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