A Five-Point Finite Difference Method for Solving Parabolic Partial Differential Equations

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A five-point finite-difrerence procedure is presented which can be used to solve partial differential equations involving time or time-like derivatives and two spatial conditions (i.e. parabolic partial differential equations). Fourth-order accuracy is obtained by approximating the time derivative by five-point central finite differences and solving the resulting system of equations implicitly. The 1- and 2-D diffusion equations are solved to illustrate the procedure.

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