Centre de Recherches Mathematiques, Universite de Montreal,

C. P. 6128, Succ. Centre-ville,

Montreal, QC, H3C 3J7, CANADA

E-mail: penskoi@crm.umontreal.ca

**Discrete matrix Riccati equations with superposition
formulas**

**Abstract:**

An ordinary differential equation is said to have a superposition formula
if its general solution can be expressed as a function of a finite number
of particular solution. Nonlinear ODE's with superposition formulas include
matrix Riccati equations. Here will shall describe discretizations of Riccati
equations that preserve the
superposition formulas. The approach is general enough to include *q*-derivatives
and standard discrete derivatives. The work was done jointly with Pavel
Winternitz.