MONDAY, December 9, 2002
Time: 9:00 AM
Constant Hall Room 1043

Ph.D. Defense
Title: Multi-Symplectic Integrators for Nonlinear Wave Equations

Alvaro Islas
Department of Mathematics & Statistics, Old Dominion University

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 two multi-symplectic discretizations based on finite differences and Fourier spectral approximations as well as a backward error analysis for multi-symplectic PDEs.