Construction of multi-symplectic algorithm for IMBq equation. (Chinese. English summary) Zbl 1091.65124
Summary: The multi-symplectic Hamiltonian formulation for nonlinear improved modified Boussinesq (IMBq) equation is considered, and the Preissman multi-symplectic integrator is deduced via implicit midpoint rule. Through eliminating middle variables, we get a new scheme which is equivalent to the Preissman multi-symplectic integrator. Moreover, we prove that it satisfies discrete multi-symplectic conservation law. In the end, we carry out some numerical experiments to illustrate its validity.
MSC:
65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
37K05 | Hamiltonian structures, symmetries, variational principles, conservation laws (MSC2010) |
65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |