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  2. Chapman–Kolmogorov equation - Wikipedia

    en.wikipedia.org/wiki/Chapman–Kolmogorov_equation

    As a corollary, it follows that to calculate the transition matrix of jump t, it is sufficient to raise the transition matrix of jump one to the power of t, that is =. The differential form of the Chapman–Kolmogorov equation is known as a master equation.

  3. Darcy friction factor formulae - Wikipedia

    en.wikipedia.org/wiki/Darcy_friction_factor_formulae

    Churchill equation [24] (1977) is the only equation that can be evaluated for very slow flow (Reynolds number < 1), but the Cheng (2008), [25] and Bellos et al. (2018) [8] equations also return an approximately correct value for friction factor in the laminar flow region (Reynolds number < 2300). All of the others are for transitional and ...

  4. Viscosity models for mixtures - Wikipedia

    en.wikipedia.org/wiki/Viscosity_models_for_mixtures

    This functional relationship is described by a mathematical viscosity model called a constitutive equation which is usually far more complex than the defining equation of shear viscosity. One such complicating feature is the relation between the viscosity model for a pure fluid and the model for a fluid mixture which is called mixing rules.

  5. Chapman–Enskog theory - Wikipedia

    en.wikipedia.org/wiki/Chapman–Enskog_theory

    The difference in this equation from classical Chapman–Enskog theory lies in the streaming operator , within which the velocity distribution of the two particles are evaluated at different points in space, separated by , where is the unit vector along the line connecting the two particles centre of mass.

  6. Difference Equations: From Rabbits to Chaos - Wikipedia

    en.wikipedia.org/wiki/Difference_Equations:_From...

    After an introductory chapter on the Fibonacci numbers and the rabbit population dynamics example based on these numbers that Fibonacci introduced in his book Liber Abaci, the book includes chapters on homogeneous linear equations, finite difference equations and generating functions, nonnegative difference equations and roots of characteristic polynomials, the Leslie matrix in population ...

  7. 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".

  8. Difference engine - Wikipedia

    en.wikipedia.org/wiki/Difference_engine

    A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions. It was designed in the 1820s, and was created by Charles Babbage . The name difference engine is derived from the method of finite differences , a way to interpolate or tabulate functions by using a small set of polynomial co-efficients.

  9. MacCormack method - Wikipedia

    en.wikipedia.org/wiki/MacCormack_method

    The application of MacCormack method to the above equation proceeds in two steps; a predictor step which is followed by a corrector step. Predictor step: In the predictor step, a "provisional" value of u {\displaystyle u} at time level n + 1 {\displaystyle n+1} (denoted by u i p {\displaystyle u_{i}^{p}} ) is estimated as follows