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4.2 The Finite Difference Method

Perhaps the most traditional way to solve (1) utilizes the finite difference approach by discretizing the solution domain using a grid of quadralaterals (for 2D) or cubes (for 3D). The coordinates of a typical grid point are , and the value of at a grid point is denoted by . Taylor's theorem can then be utilized to provide the difference equations (see the section on Some High Performance Computing Issues in Partial Differential Equationsgif). For example:

with similar equations for .