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A symplectic algorithm for wave equations

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  • Lu, Xiaowu
  • Schmid, Rudolf

Abstract

Numerical schemes for finite-dimensional Hamiltonian system which preserve the symplectic structure are generalized to infinite-dimensional Hamiltonian systems and applied to construct finite difference schemes for the nonlinear wave equation. The numerical results show that these schemes compare favorably with conventional difference methods. Furthermore, the successful long-term tracking capability for these Hamiltonian schemes is remarkable and striking.

Suggested Citation

  • Lu, Xiaowu & Schmid, Rudolf, 1997. "A symplectic algorithm for wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(1), pages 29-38.
    • Handle: RePEc:eee:matcom:v:43:y:1997:i:1:p:29-38
    DOI: 10.1016/S0378-4754(96)00052-3
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    Cited by:

    1. Lu, Xiaowu, 2001. "Symplectic computation of solitary waves for general Sine–Gordon equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 55(4), pages 519-532.
    2. Brugnano, L. & Frasca Caccia, G. & Iavernaro, F., 2015. "Energy conservation issues in the numerical solution of the semilinear wave equation," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 842-870.
    3. Lu, Xiaowu & Schmid, Rudolf, 1999. "Symplectic integration of Sine–Gordon type systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 50(1), pages 255-263.

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