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I would like to ask, if any general method of solving systems of partial difference (not differential) equations is known, at least for some classes of systems. For instance, for ordinary difference equations, there is a general method of solving homogenous systems of first-order linear O$\Delta$E's with constant coefficients. Can it be extended to P$\Delta$E's? Or, equivalently, is there any general method of solving infinite homogenous systems of first-order linear O$\Delta$E's with constant coefficients?

Thank you in advance.

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