### Applied Mathematics Seminar

Department of Mathematics, University of Texas at Arlington

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__Date/Time/Room:__ Tuesday (11/28/2000) at 3:30 pm in 487 Pickard Hall
(Refreshments served at 3:00 pm)

__Speaker:__
Bruno D. Welfert,
Department of Mathematics,
Arizona State University

*``A nonstandard Euler scheme for
y"+g(y)y'+f(y)y=0''*

**Abstract:**
We introduce a nonstandard Euler scheme for solving the differential
equation y"+g(y)y'+f(y)y=0 which has the same linear stability
properties
as the differential equation and is conservative when g=0. The method is
based on a physically motivated reduction of the equations to a system
of
two first order equations and the use of Lie group integrators. The
method is demonstrated on a few examples and compared to other schemes,
including a symmetric standard scheme and a MATLAB adaptive solver.