Multi-symplectic Runge-Kutta-type methods for Hamiltonian wave equations. (English) Zbl 1100.65117
The nonlinear wave equation is taken as a model problem for the investigation. Different multi-symplectic reformulations of the equation are discussed. Multi-symplectic Runge-Kutta methods and multi-symplectic partitioned Runge-Kutta methods are explored based on these different reformulations. Some popular and efficient multi-symplectic schemes are collected and constructed. Stability analyses are performed for these schemes.
Reviewer: Anna Maria Cherubini (Lecce)
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
