Abstract
Recently the field of numerical analysis experienced a growing interest in the numerical investigation of ordinary and partial differential equations (pde’s) by using geometric integrators which preserve the essential features of the underlying system after discretization. Symplectic integrators for ordinary differential equations (ode’s) have been thoroughly analyzed and the concept of symplectic time integration has also been extended to Hamiltonian pde’s [7,13]. More recently nonlinear pde’s were also studied numerically using multi-symplectic integrators (see [3,13] for an overview). A multi-symplectic structure of a pde is generated by a pair of skewsymmetric matrices M,K ∈ Rn×nand a multi-symplectic Hamiltonian S(z) which is a smooth function on R:
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