Abstract
The Finite Difference (FD) method is the simplest numerical method to solve Partial Differential Equations (PDE) in regions bounded by simple as well as by complex geometries. It is based on the assumption that the continuous physical space is replaced by a space subdivided into a grid where the unknowns are located at certain location of the cell. The grid suitable to FD is a structured or regular grid, where each point is numbered consecutively and is identified by a set of indices, e.g. (i,j,k). This passage from a continuous to a discrete space leads to the substitution of the differential operators by algebraic operators. When the decision has been taken to move into the discrete space, each further equation derived by applying differential operators to the original equations should be obtained by applying the algebraic operators.KeywordsElliptic EquationCoarse GridTruncation ErrorMultigrid MethodDirect SolverThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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