Discrete matrix Riccati equations with superposition formulas

Details Discrete matrix Riccati equations with superposition formulas Discrete matrix Riccati equations with superposition formulas

2003-05-25

arxiv.org/abs/math-ph/0305053v2

J. Math. Anal. Appl. 294 (2004) 533-547

Physics

Mathematical Physics

20 pages; v.2: a misprint corrected

Scientific paper

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.

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