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

Helen M. Regan

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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 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 spatisl step size.

  • Keywords

symplectic integration Hamiltonian PDEs linear stability von Neumann analysis

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@Article{JCM-20-611, author = {}, 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 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 spatisl 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 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 KW - Hamiltonian PDEs KW - linear stability KW - 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 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 spatisl step size.
Helen M. Regan. (1970). Von Neumann Stability Analysis of Symplectic Integrators Applied to Hamiltonian PDEs. Journal of Computational Mathematics. 20 (6). 611-618. doi:
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