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Volume 20, Issue 6
Von Neumann Stability Analysis of Symplectic Integrators Applied to Hamiltonian PDEs

Helen M. Regan

J. Comp. Math., 20 (2002), pp. 611-618.

Published online: 2002-12

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  • Abstract

Symplectic integration of separable Hamiltonian ordinary and partial differential equations is discussed. A von Neumann analysis is performed to achieve general linear stability criteria for symplectic methods applied to a restricted class of Hamiltonian PDEs. In this treatment, the symplectic step is performed prior to the spatial step, as opposed to the spatial, as opposed to the standard approach of spatially discretising the PDE to form a system of Hamiltonian ODEs to which a symplectic integrator can be applied. In this way stability criteria are achieved by considering the spectra of linearised Hamiltonian PDEs rather than spatial step size.

  • Keywords

symplectic integration, Hamiltonian PDEs, linear stability, von Neumann analysis.

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COPYRIGHT: © Global Science Press

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@Article{JCM-20-611, author = {Helen M. Regan}, title = {Von Neumann Stability Analysis of Symplectic Integrators Applied to Hamiltonian PDEs}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {6}, pages = {611--618}, abstract = {

Symplectic integration of separable Hamiltonian ordinary and partial differential equations is discussed. A von Neumann analysis is performed to achieve general linear stability criteria for symplectic methods applied to a restricted class of Hamiltonian PDEs. In this treatment, the symplectic step is performed prior to the spatial step, as opposed to the spatial, as opposed to the standard approach of spatially discretising the PDE to form a system of Hamiltonian ODEs to which a symplectic integrator can be applied. In this way stability criteria are achieved by considering the spectra of linearised Hamiltonian PDEs rather than spatial step size.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8946.html} }
TY - JOUR T1 - Von Neumann Stability Analysis of Symplectic Integrators Applied to Hamiltonian PDEs AU - Helen M. Regan JO - Journal of Computational Mathematics VL - 6 SP - 611 EP - 618 PY - 2002 DA - 2002/12 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8946.html KW - symplectic integration, Hamiltonian PDEs, linear stability, von Neumann analysis. AB -

Symplectic integration of separable Hamiltonian ordinary and partial differential equations is discussed. A von Neumann analysis is performed to achieve general linear stability criteria for symplectic methods applied to a restricted class of Hamiltonian PDEs. In this treatment, the symplectic step is performed prior to the spatial step, as opposed to the spatial, as opposed to the standard approach of spatially discretising the PDE to form a system of Hamiltonian ODEs to which a symplectic integrator can be applied. In this way stability criteria are achieved by considering the spectra of linearised Hamiltonian PDEs rather than spatial step size.

Helen M. Regan. (2002). Von Neumann Stability Analysis of Symplectic Integrators Applied to Hamiltonian PDEs. Journal of Computational Mathematics. 20 (6). 611-618. doi:
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