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Methods for the approximate solution of differential equations based on replacing them by equations involving functions of a discrete variable. See [[Hyperbolic partial differential equation, numerical methods|Hyperbolic partial differential equation, numerical methods]]; [[Parabolic partial differential equation, numerical methods|Parabolic partial differential equation, numerical methods]]; [[Elliptic partial differential equation, numerical methods|Elliptic partial differential equation, numerical methods]]; [[Differential equations, ordinary, approximate methods of solution of|Differential equations, ordinary, approximate methods of solution of]].