Exponential monotonicity of quadratic forms in ODEs and preserving methods

Cinzia Elia, Luciano Lopez

School of Mathematics, Georgia Tech, Atlanta, GA 30332, U.S.A.
Dipartimento di Matematica, Univ. of Bari, I-70100, Bari, Italy

elia@math.gatech.edu, lopez@pascal.dm.uniba.it

Contributed talk

In this work we study ordinary differential equations whose solutions $Y(t)$ satisfy the following monotonic quadratic form: $Y(t)^THY(t)=e^{-\alpha t}Y(t_0)^THY(t_0)$, where $H$ is an orthogonal matrix and $\alpha > 0$. Numerical methods preserving this exponential decay are investigated.