Abstract
ABSTRACTWe present a general and effective method, known as the Fokas method, to solve an arbitrary discrete linear evolution equation posed in a finite lattice. The method is based on the simultaneous analysis of both parts of Lax pair, as well as the global relation that involves initial and boundary values. We show that, as in the continuum problems, the method can be applied effectively to solve general linear differential-difference equations in a finite lattice. In particular, we demonstrate the method by addressing a number of significant examples and we discuss the continuum limits of the solution and the boundary values.
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