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Partitioned Runge-Kutta methods in space and time

Friday 6th July 2007 - 09:00 to 10:00
INI Seminar Room 1

In a partitioned RK (PRK) method, different coefficients are used for different variables. This allows, for example, explicit symplectic integrators for separable Hamiltonians; in fact, these are a special case of splitting methods. There also exist implicit symplectic PRK methods, but these seem to have no clear application, since non- partitioned (Gauss) methods dominate them. Recently, a possible application has emerged for implicit symplectic PRK methods in the spatial discretization of Hamiltonian PDEs. Here they can yield stable multisymplectic methods, while by contrast, explicit PRK methods are unconditionally unstable.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons