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  2. Finite difference - Wikipedia

    en.wikipedia.org/wiki/Finite_difference

    In an analogous way, one can obtain finite difference approximations to higher order derivatives and differential operators. For example, by using the above central difference formula for f ′(x + ⁠ h / 2 ⁠) and f ′(x − ⁠ h / 2 ⁠) and applying a central difference formula for the derivative of f ′ at x, we obtain the central difference approximation of the second derivative of f:

  3. Finite difference method - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_method

    To use a finite difference method to approximate the solution to a problem, one must first discretize the problem's domain. This is usually done by dividing the domain into a uniform grid (see image). This means that finite-difference methods produce sets of discrete numerical approximations to the derivative, often in a "time-stepping" manner.

  4. Finite difference coefficient - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_coefficient

    For arbitrary stencil points and any derivative of order < up to one less than the number of stencil points, the finite difference coefficients can be obtained by solving the linear equations [6] ( s 1 0 ⋯ s N 0 ⋮ ⋱ ⋮ s 1 N − 1 ⋯ s N N − 1 ) ( a 1 ⋮ a N ) = d !

  5. Five-point stencil - Wikipedia

    en.wikipedia.org/wiki/Five-point_stencil

    An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".

  6. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    The simplest method is to use finite difference approximations. ... For example, [5] the first derivative can be calculated by the complex-step derivative formula: ...

  7. Central differencing scheme - Wikipedia

    en.wikipedia.org/wiki/Central_differencing_scheme

    Figure 1.Comparison of different schemes. In applied mathematics, the central differencing scheme is a finite difference method that optimizes the approximation for the differential operator in the central node of the considered patch and provides numerical solutions to differential equations. [1]

  8. Nine-point stencil - Wikipedia

    en.wikipedia.org/wiki/Nine-point_stencil

    It is used to write finite difference approximations to derivatives at grid points. It is an example for numerical differentiation. This stencil is often used to approximate the Laplacian of a function of two variables. An illustration of the nine-point stencil in two dimensions.

  9. MacCormack method - Wikipedia

    en.wikipedia.org/wiki/MacCormack_method

    In computational fluid dynamics, the MacCormack method (/məˈkɔːrmæk ˈmɛθəd/) is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack in 1969. [1]