Numerical implementation of the multisymplectic Preissman scheme and its equivalent schemes. (English) Zbl 1047.65107

The authors construct some new methods for solving the Korteweg-de Vries equation. They introduce an artificial boundary condition that makes the implementation of the Preissman scheme practical. More efficient implementations are also considered. Furthermore, by eliminating the auxiliary variables an 8 point and a 12 point explicit method is constructed. While not multisymplectic, numerical results on soliton behaviour confirm the effectiveness of these methods and variants on the multisymplectic Preissman methods.


65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
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