Spectral variational integrators for semi-discrete Hamiltonian wave equations. (English) Zbl 1367.65192
Summary: In this paper, we present a highly accurate Hamiltonian structure-preserving numerical method for simulating Hamiltonian wave equations. This method is obtained by applying spectral variational integrators (SVI) to the system of Hamiltonian ordinary differential equations (ODEs) which are derived from the spatial semi-discretization of the Hamiltonian partial differential equation (PDE). The spatial variable is discretized by using high-order symmetric finite-differences. An efficient implementation of SVI for high-dimensional systems of ODEs is presented.
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
spectral variational integrator; semi-discrete; symmetric difference; Hamiltonian wave equationsReferences:
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