Solutions of Non-linear Differential and Difference Equations with Superposition Formulas
arXiv:solv-int/9905003
Abstract
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit solutions of certain classes of scalar and matrix Riccati equations are presented as an illustration of the general results.
17 pages, REVTeX, submitted to Journ.Math.Phys