2003/05/31 by Alexei V. Penskoi, Pavel Winternitz
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:34A34 #msc:39A12
published as J. Math. Anal. Appl. 294 (2004) 533-547 · 20 pages; v.2: a misprint corrected
arxiv created 2004/03/25 · arxiv updated 2009/11/30
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 we shall describe discretizations of Riccati equations that preserve the superposition formulas. The approach is general enough to include q-derivatives and standard discrete derivatives.