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The MacCormack method is designed to solve hyperbolic partial differential equations of the form. To update this equation one timestep on a grid with spacing at grid cell , the MacCormack method uses a "predictor step" and a "corrector step", given below [3]
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak ...
The Bogacki–Shampine method is a Runge–Kutta method of order three with four stages with the First Same As Last (FSAL) property, so that it uses approximately three function evaluations per step. It has an embedded second-order method which can be used to implement adaptive step size.
If these 's are independent, then a test for can be developed by the following procedure, known as Šidák correction. Step 1, we test each of m null hypotheses at level ().
In statistics, the Šidák correction, or Dunn–Šidák correction, is a method used to counteract the problem of multiple comparisons. It is a simple method to control the family-wise error rate.
Prentice's rule, named so after the optician Charles F. Prentice, is a formula used to determine the amount of induced prism in a lens: = where: P is the amount of prism correction (in prism dioptres) c is decentration (the distance between the pupil centre and the lens's optical centre, in millimetres)
NEW YORK — Emma Hayes peered out the window of a third-floor conference room overlooking Madison Avenue, out across the bustling city where her coaching career first bloomed, and memories came ...
PISO algorithm ( Pressure-Implicit with Splitting of Operators) was proposed by Issa in 1986 without iterations and with large time steps and a lesser computing effort. It is an extension of the SIMPLE algorithm used in computational fluid dynamics to solve the Navier-Stokes equations.
In particular, for non-magnetic materials ( μ = μ0 ), the susceptibility χ that appears in the Kramers–Kronig relations is the electric susceptibility χe = n2 − 1. The most commonly seen consequence of dispersion in optics is the separation of white light into a color spectrum by a prism.
The radiative transfer equation is a monochromatic equation to calculate radiance in a single layer of the Earth's atmosphere. To calculate the radiance for a spectral region with a finite width (e.g., to estimate the Earth's energy budget or simulate an instrument response), one has to integrate this over a band of frequencies (or wavelengths).