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LREtools

  

riccati

  

find solutions of Riccati Recurrence equations

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

riccati(problem)

Parameters

problem

-

problem statement or RESol

Description

• 

Attempts to solve Riccati recurrence equations using various substitutions.

• 

A Riccati recurrence equation in y(k) is one of the form yk+1yk+Akyk+1+Bkyk=Ck where A(k), B(k), and C(k) are independent of y(k).  If the equation is homogeneous (Ck=0), then we try the substitution xk=1yk, which makes the equation first order linear and if not, then we try yk=xkBkxk+1xk+1, which makes the equation second order linear. Finally, there is the substitution yk=xk+1Ak+1xkxk, 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.

Examples

withLREtools:

probREcreateyk+1yk+2yk+13yk=1,yk,y0=12

prob:=RESolyk+13yk+2yk+1=1,yk,y0=12,INFO

(1)

riccatiprob

1255k55+5k5+55k+5+5k55k+5+5k

(2)

riccatiyk+1yk+2yk+1kyk=0,yk,

charfcn0ky0

(3)

See Also

LREtools

LREtools[REcreate]

RESol

rsolve

 


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