On the numerical approximation of algebraic equations with symmetries
 
 
Description: 
The resolution of systems of algebraic equations with symmetry groups appears in the mathematical treatment of many models, [1, 2]. These groups consist of transformations that map solutions of the algebraic system into other solutions. Some consequences of the existence of such symmetry groups, from an analytical point of view, have been described in e. g. [2]. The main goal of this talk is discussing the influence of the symmetries in the numerical procedures to approximate the solutions of the systems, by introducing the concept of orbital convergence. Many of the applications of these ideas involve the approximation of differential equations with symmetries; in this sense, the numerical generation of travelling wave solutions of nonlinear dispersive wave equations will be considered to illustrate the results.

References
[1] Marsden, J.E., Ratiu, T.S.: Introduction to Mechanics and Symmetry, Springer, New York (1994)
[2] Olver, P.J.: Applications of Lie Groups to Differential Equations, Springer, New York (1986)
Date:  2014-05-21
Start Time:   14:30
Speaker:  Angel Durán (Univ. Valladolid, Spain)
Institution:  University of Valladolid
Place:  Room 5.4 (DMUC)
Research Groups: -Numerical Analysis and Optimization
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