Attempts to solve Riccati recurrence equations using various substitutions.

A Riccati recurrence equation in y(k) is one of the form  where A(k), B(k), and C(k) are independent of y(k).  If the equation is homogeneous (), then we try the substitution , which makes the equation first order linear and if not, then we try , which makes the equation second order linear. Finally, there is the substitution , which makes the equation second order linear. If rsolve can solve these new equations, then we back-substitute to obtain solutions to the original problems.

If A(k) is undefined for some k, then a set of equations may be returned, giving values of y(k) for specific k as well as the general formula.

Since it calls rsolve, this procedure can be expensive; because of the back-substitution, the answers may be overly complicated.

See the help page for LREtools[REcreate] for the definition of the format of a problem.