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Continuous numerical methods have many applications in the numerical solution of discontinuous ordinary differential equations, delay differential equations, delay differential-algebraic equations, neutral delay differential equations, integro-.
In this paper, we study the integration of Hamiltonian wave equations whose solutions have oscillatory behaviors in time and/or space. We are mainly concerned with the research for multi-symplectic extended Runge-Kutta-Nystrom (ERKN) discretizations and .
A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation which can be viewed as a generalization of the symplectic structure of Hamiltonian ODEs. We show that Gauss Legendre collocation in space and time leads .