Finite difference is a numerical method used to approximate solutions to differential equations by discretizing the equations and evaluating them at specific points. It is commonly applied in numerical analysis, engineering, and scientific computing to estimate derivatives and solve problems involving functions defined on discrete sets of points. In the context of approximating derivatives, the finite difference method works by replacing the derivatives in the differential equation with finite difference approximations.
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A finite difference compares the values of a function at finitely separated arguments. For example, the forward finite difference with step isIt is the discrete analogue of a derivative and lowers the degree of a nonconstant polynomial by one.