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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2002-2003 MATHEMATICS COLLOQUIUM SERIES 11/26/02 Colloquium MR. ALVARO ISLAS Department of Mathematics Old Dominion University Multisymplectic PDE Integrators Abstract:   Symplectic integrators for Hamiltonian ODEs have shown to be robust, efficient and accurate in long-term calculations. Insight into the performance of symplectic methods has been provided by a backward error analysis of the problem. In this talk, we extend these ideas to Hamiltonian PDEs. We introduce the concept of multi-symplectic PDEs and present several examples to illustrate how it applies to well known nonlinear equations. Local conservation laws of multi-symplecticity, energy and momentum will be discussed. We present t2wo mulit-symplectic discretizations based on finite differences and Fourier spectral approximations as well as a backward error analysis for multi-symplectic PDEs.