Systems of partial difference equations

I have been wondering, if there is any universal method of solving some special classes of systems of partial difference equations.

For instance, there is an universal method of solving systems of homogenous systems of linear first-order ordinary difference equations with constant coefficients. Can it be extended to partial difference equations? Or equivalently, is there any universal method of solving infinite homogenous systems of linear first-order ordinary difference equations with constant coefficients?

Thank you in advance.

flag	asked Sep 7 2011 at 13:07 042 43●3

I'm not sure this question is appropriate for MO, but here's the short answer: You can solve linear first order constant coefficient ODE x' = Ax by the matrix exponential x(t) = e^(At)x(0). In the PDE or infinite-dimensional ODE setting the same formula works so long as the operator A is the infinitesimal generator of a semigroup. – Aaron Hoffman Sep 7 2011 at 18:00