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In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps:
The Adams–Moulton methods are solely due to John Couch Adams, like the Adams–Bashforth methods. The name of Forest Ray Moulton became associated with these methods because he realized that they could be used in tandem with the Adams–Bashforth methods as a predictor-corrector pair (Moulton 1926); Milne (1926) had the same idea.
This is the Euler method (or forward Euler method, in contrast with the backward Euler method, to be described below). The method is named after Leonhard Euler who described it in 1768. The Euler method is an example of an explicit method. This means that the new value y n+1 is defined in terms of things that are already known, like y n.
JANUS – Adams-Moulton predictor-corrector for non-differential-propagating contexts; MERCURY – Gears rate/state differentiating stiff and step-size optimizing method for non-differential-propagating contexts; MERLIN – self-starting technique of rational function extrapolation from Gragg, Bulirsch, and Stoer with differential propagation;
Adams method may refer to: A method for the numerical solution of ordinary differential equations, also known as the linear multistep method A method for apportionment of seats among states in the parliament, a kind of a highest-averages method
Hamming developed an improved version, the Hamming predictor-corrector. This was in use for many years, but has since been superseded by the Adams method . [ 16 ] He did extensive research into digital filters , devising a new filter, the Hamming window , and eventually writing an entire book on the subject, Digital Filters (1977).
Mehrotra's predictor–corrector method in optimization is a specific interior point method for linear programming.It was proposed in 1989 by Sanjay Mehrotra. [1]The method is based on the fact that at each iteration of an interior point algorithm it is necessary to compute the Cholesky decomposition (factorization) of a large matrix to find the search direction.
The Euler method often serves as the basis to construct more complex methods, e.g., predictor–corrector method. ... as illustrated by the two-step Adams–Bashforth ...