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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.

MSC:
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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