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Conformal multi-symplectic integration methods for forced-damped semi-linear wave equations

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  • Moore, Brian E.

Abstract

Conformal symplecticity is generalized to forced-damped multi-symplectic PDEs in 1+1 dimensions. Since a conformal multi-symplectic property has a concise form for these equations, numerical algorithms that preserve this property, from a modified equations point of view, are available. In effect, the modified equations for standard multi-symplectic methods and for space-time splitting methods satisfy a conformal multi-symplectic property, and the splitting schemes exactly preserve global symplecticity in a special case. It is also shown that the splitting schemes yield incorrect rates of energy/momentum dissipation, but this is not the case for standard multi-symplectic schemes. These methods work best for problems where the dissipation coefficients are small, and a forced-damped semi-linear wave equation is considered as an example.

Suggested Citation

  • Moore, Brian E., 2009. "Conformal multi-symplectic integration methods for forced-damped semi-linear wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(1), pages 20-28.
    • Handle: RePEc:eee:matcom:v:80:y:2009:i:1:p:20-28
    DOI: 10.1016/j.matcom.2009.06.024
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