QIN Yu-yue, DENG Zi-chen, HU Wei-peng. Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System[J]. Applied Mathematics and Mechanics, 2014, 35(1): 22-28. doi: 10.3879/j.issn.1000-0887.2014.01.003
Citation: QIN Yu-yue, DENG Zi-chen, HU Wei-peng. Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System[J]. Applied Mathematics and Mechanics, 2014, 35(1): 22-28. doi: 10.3879/j.issn.1000-0887.2014.01.003

Structure-Preserving Algorithm for Steady-State Solution to the Infinite Dimensional Hamilton System

doi: 10.3879/j.issn.1000-0887.2014.01.003
Funds:  The National Natural Science Foundation of China(11172239;11372252;11372253)
  • Received Date: 2013-10-15
  • Rev Recd Date: 2013-10-22
  • Publish Date: 2014-01-15
  • Based on Hamilton variational principle and Bridges’ multi-symplectic integration theory, a new structure-preserving algorithm was proposed to simulate the steady-state solution to the complex infinite dimensional Hamilton system. With Zufiria’s Boussinesq-type equations as an example, the high-order partial differential equation describing the steady-state solution to the Zufiria model was rewritten into a symmetric form under the energy flux conservation law and momentum flux conservation law firstly; then the box scheme for the symmetric form was constructed to simulate the steady-state solution to the Zufiria model. The numerical results show that the box scheme can well simulate the steady-state solution to the Zufiria model while properly preserving the momentum flux conservation law.
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