- #1
Adeimantus
- 113
- 1
Is there a general method for solving 2-index recurrence relations with constant coefficients? Here is one I would like to solve
[tex]a_{m,n} = \frac{xa_{m-1,n} + ya_{m,n-1} + 1}{x+y}[/tex] for m,n > 0
with initial conditions
[tex]a_{m,0} = m/x[/tex] and [tex]a_{0,n} = n/y[/tex].
Hoping for an analogy with PDE's, I tried separation of variables for the homogeneous part of the solution: [tex]a^h_{m,n} = M_mN_n[/tex]. But I couldn't figure out how to match the initial conditions. I don't think that is the right approach.
thanks :)
[tex]a_{m,n} = \frac{xa_{m-1,n} + ya_{m,n-1} + 1}{x+y}[/tex] for m,n > 0
with initial conditions
[tex]a_{m,0} = m/x[/tex] and [tex]a_{0,n} = n/y[/tex].
Hoping for an analogy with PDE's, I tried separation of variables for the homogeneous part of the solution: [tex]a^h_{m,n} = M_mN_n[/tex]. But I couldn't figure out how to match the initial conditions. I don't think that is the right approach.
thanks :)