Abstract
The direct use of integral transforms. or operational calculus. is well-known for solvng differential equations associated with initial or boundary conditions. Their advantage lies in transforming the given differential equation to a simpler algebraic equation: they also incorporate the initial or boundary conditions at the outset. The Laplace transform method involves the initial conditions,while the Fourier transform method involves a variety of boundary conditions. The ztransform as the discree analog of Laplace transform. is used in solving linear difference equations wih intial conditions. In this paper. we introduce the operational sum calculus method of the discrete Fourier transform (DFT)for sloving (linear) difference equations with generally nonhomogeneous boundary conditions. In contrast with using the difficult numerical inversion of thez-transform.the discrete Fourier ransforms enjoy the Fast Fourier transform (TFT)algorithms.
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