IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Some New Structure-Preserving Algorithms for Multi-symplectic Hamiltonian PDEs

  • Feb. 15, 2016
  • 1:15 p.m.
  • LeConte 312

Abstract

Many partial differential equations (PDEs) can be written as a multi-symplectic Hamiltonian system, which has three local conservation laws, namely multi-symplectic conservation law, local energy conservation law and local momentum conservation law. This talk gives several systematic methods for discretizing general multi-symplectic formulations of Hamiltonian PDEs, including a class of multi-symplectic methods, a class of global energy-preserving methods, a local energy-preserving algorithm and a local momentum-preserving algorithm. The methods are illustrated by the nonlinear Schrodinger equation and the Korteweg-de Vries equation. Numerical experiments are presented to demonstrate the conservative properties of the proposed numerical methods.

Key words: Structure-preserving algorithm, Multi-symplectic, Energy-preserving, Momentum-preserving, Hamiltonian PDEs.

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