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  2. Backward differentiation formula - Wikipedia

    en.wikipedia.org/wiki/Backward_differentiation...

    The backward differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations.They are linear multistep methods that, for a given function and time, approximate the derivative of that function using information from already computed time points, thereby increasing the accuracy of the approximation.

  3. Finite difference coefficient - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_coefficient

    For example, the third derivative with a second-order accuracy is ... The theory of Lagrange polynomials provides explicit formulas for the finite difference ...

  4. Probability of superiority - Wikipedia

    en.wikipedia.org/wiki/Probability_of_superiority

    In other words, the correlation is the difference between the common language effect size and its complement. For example, if the common language effect size is 60%, then the rank-biserial r equals 60% minus 40%, or r = 0.20. The Kerby formula is directional, with positive values indicating that the results support the hypothesis.

  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 classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.

  7. 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:

  8. Compact finite difference - Wikipedia

    en.wikipedia.org/wiki/Compact_finite_difference

    The classical Pade scheme for the first derivative at a cell with index (′) reads; ′ + ′ + + ′ = +. Where is the spacing between points with index , & +.The equation yields a fourth-order accurate solution for ′ when supplemented with suitable boundary conditions (typically periodic).

  9. Stencil (numerical analysis) - Wikipedia

    en.wikipedia.org/wiki/Stencil_(numerical_analysis)

    The finite difference coefficients for a given stencil are fixed by the choice of node points. The coefficients may be calculated by taking the derivative of the Lagrange polynomial interpolating between the node points, [3] by computing the Taylor expansion around each node point and solving a linear system, [4] or by enforcing that the stencil is exact for monomials up to the degree of the ...