Multi-symplectic algorithms for Hamiltonian partial differential equations. (English) Zbl 1289.65278
Summary: Recently, multi-symplectic discretizations of Hamiltonian partial differential equations (PDEs) are drawing much attention and therefore they become the vigorous component of the structure-preserving algorithms. This paper reviews the development of multi-symplectic algorithms for Hamiltonian PDEs, which include the basic concepts, some main results, and their applications. Several generalizations are also described.
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) |
