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 equation 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 a standard M ATL AB adaptive solver.
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