predictor-corrector methods

predictor-corrector methods

[′pri¦dik·tər kə′rek·tər ‚meth·ədz]
(mathematics)
Methods of calculating numerical solutions of differential equations that employ two formulas, the first of which predicts the value of the solution function at a point x in terms of the values and derivatives of the function at previous points where these have already been calculated, enabling approximations to the derivatives at x to be obtained, while the second corrects the value of the function at x by using the newly calculated values.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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After explaining its basic properties, they describe its use in explicit Runte-Kutta methods, linear multi-step and predictor-corrector methods, some implicit methods, splitting techniques, advection problems, and other problems.
In some cases, the accuracy of LMMs is low such as the case of predictor-corrector methods which incur high computational rigour.
To avoid solving nonlinear equations, the predictor-corrector methods of the two schemes are proposed in Section 5.
Adams predictor-corrector methods are recommended for simulating systems with an easy or moderate stiff behavior.
KHALIQ, A linearlyimplicit predictor-corrector methods for reaction-diffusion equations, Comput.
In recent years, Noor [15]-[27] and Noor-Noor and Rassias [28] have used this technique to study some predictor-corrector methods for various classes of equilibrium and variational inequality problems.
Examples of the multistep methods are the predictor-corrector methods of Adams Bashforth and Moulton.
They are usually implemented as predictor-corrector methods using both an explicit and an implicit method to calculate [y.sub.n+k].
Our objective is to present a BHTRKNM that is implemented in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods (see Jator et al.
Noor: Predictor-corrector methods for multi-valued hemiequilibrium problems, Appl.
Statter, Generalized multi-step predictor-corrector methods, ACM, 11, pp.
h [err.sub.rel] [AB2.sup.*] [err.sub.rel] [FE.sup.*] 2e-l 1.03-1 1.02e-l le-1 8.73e-3 6.72e-2 5e-2 3.64e-3 3.98e-2 2.5e-2 1.28e-3 2.16e-2 1.25e-2 3.63e-4 1.12e-2 6.25e-3 9.71e-5 5.65e-3 h [err.sub.rel] AB2 [err.sub.rel] FE 2e-l NaN NaN le-1 NaN NaN 5e-2 NaN NaN 2.5e-2 NaN NaN 1.25e-2 NaN 6.65e-3 6.25e-3 5.65e-5 3.33e-3 Table 4.2 Relative errors using different time-steps for the predictor-corrector methods [AB2.sup.*]-[CN.sup.*], [FE.sup.*]-[CN.sup.*].

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