DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Jean-Philippe Lessard, Université Laval

**Title: ***
Computation of solutions of nonlinear differential equations using Chebyshev series and rigorous numerics
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**Abstract:**
A computational method based on Chebyshev series to rigorously compute solutions of initial and boundary value problems of nonlinear differential equations is proposed. The idea is to recast solutions as fixed points of an operator defined on a Banach space of rapidly decaying Chebyshev coefficients and to combine analytic estimates and the contraction mapping theorem to show the existence of a unique fixed point nearby an approximate solution. As applications, solutions of the Ginzburg-Landau equation, solutions of initial value problems in the Lorenz equations and symmetric connecting orbits in the Gray-Scott equation are rigorously computed. This is joint work with Anais Correc (Laval) and Christian Reinhardt (TU Munich).

**Time:** Friday, April 19, 2013, 1:30-2:30 p.m.

**Place:** Planetary Hall (formerly S & T I), Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491