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** Adams-Moulton predictor-corrector method **

** Differential equations predictor-corrector method **

** Gear predictor corrector method **

** Gear predictor-corrector integration method **

** Potential predictor-corrector methods of molecular **

In the predictor - corrector methods the magnitude of the first correction is an immediate error estimate with no additional cost. [Pg.272]

Numerous predictor-corrector methods have been developed over the years. A simple second order predictor-corrector method can be constructed by first approximating the solution at the new time step using the first order explicit Euler method [Pg.1021]

One way to do this is afforded by the predictor-corrector method. We ignore terms higher than those shown explicitly, and calculate the predicted terms starting with bP(t). However, this procedure will not give the correct trajectory because we have not included the force law. This is done at the corrector step. We calculate from the new position rP the force at time t + St and hence the correct acceleration a (t -f 5t). This can be compared with the predicted acceleration aP(f -I- St) to estimate the size of the error in the prediction step [Pg.63]

This system of equations was solved by a predictor-corrector method for several values of a, / , and y using a digital computer. It was not possible to examine values of ft above 50 (a = 0.001, y = 0) as the method broke down because of accumulated errors. Up to these values, although a step is formed in the extent of reaction vs. time curve, the rate of acceleration in the third phase of the reaction was much slower than observed in the experiments. [Pg.223]

M71 Solution of ordinary differential equations predictor-corrector method of Milne 7100 7188 [Pg.14]

The great advantage of the predictor - corrector methods is that in addition to y1+, in expression (5.25) we need only previously computed (and saved) function values. Thus, the computational cost depends on the number of corrections and does not depend on the order p of the particular formula. [Pg.270]

A combination of open- and closed-type formulas is referred to as the predictor-corrector method. First the open equation (the predictor) is used to estimate a value for y,, this value is then inserted into the right side of the corrector equation (the closed formula) and iterated to improve the accuracy of y. The predictor-corrector sets may be the low-order modified (open) and improved (closed) Euler equations, the Adams open and closed formulas, or the Milne method, which gives the following system [Pg.87]

R. M. Thomas and T. E. Simos, A family of hybrid exponentially fitted predictor-corrector methods for the numerical integration of the radial Schrodinger equation, J. Comput. Appl. Math., 1997, 87, 215-226. [Pg.481]

An important question is the relative numerical efficiency of the two methods or, more generally, the two families of methods. At a fixed step size the predictor - corrector methods clearly require fewer function evaluations. This does not necessarily means, however, that the predictor - corrector methods are superior in every application. In fact, in our present example increasing the step size leaves the FTunge - Kutta solution almost unchanged, whereas the Milne solution is deteriorating as shown in Table 5.1. [Pg.271]

G. Psihoyios and T. E. Simos, The numerical solution of the radial Schrodinger equation via a trigonometrically fitted family of seventh algebraic order Predictor-Corrector methods, J. Math. Chem., 2006, 40(3), 269-293. [Pg.482]

Thus we find that the choice of quaternion variables introduces barriers to efficient symplectic-reversible discretization, typically forcing us to use some off-the-shelf explicit numerical integrator for general systems such as a Runge-Kutta or predictor-corrector method. [Pg.355]

If j30 = 0, the method is explicit and the computation of is straightforward. If 30 + 0, the method is implicit because an implicit algebraic equation is to be solved. Usually, two algorithms, a first one explicit and called the predictor, and a second one implicit and called the corrector, are used simultaneously. The global method is called a predictor-corrector method as, for example, the classical fourth-order Adams method, viz. [Pg.300]

Our discussion so far has considered the use of SHAKE with the Verlet algorithm Versions have also been derived for other integration schemes, such as the leap-froj algorithm, the predictor-corrector methods and the velocity Verlet algorithm. In the cast of the velocity Verlet algorithm, the method has been named RATTLE [Anderson 1983] [Pg.389]

These results are similar to that from the energy balance. The differences are the result of round off errors in the simple finite difference calculation scheme used here (i.e., more complicated predictor-corrector methods would yield more accurate results ). [Pg.43]

All these observations tend to favour the Verlet algoritlnn in one fonn or another, and we look closely at this in the following sections. For historical reasons only, we mention the more general class of predictor-corrector methods which have been optimized for classical mechanics simulations, [40, 4T] further details are available elsewhere [7, 42, 43]. [Pg.2250]

The temperature, pore width and average pore densities were the same as those used by Snook and van Megen In their Monte Carlo simulations, which were performed for a constant chemical potential (12.). Periodic boundary conditions were used In the y and z directions. The periodic length was chosen to be twice r. Newton s equations of motion were solved using the predictor-corrector method developed by Beeman (14). The local fluid density was computed form [Pg.266]

The multistep method (5.25) is explicit if bQ = 0, otherwise it is implicit. These latter are the best ones due to their improved stability properties. To use an implicit formula, however, we need an initial estimate of yi+1. The basic idea of the predictor - corrector methods is to estimate y1+1 by a p-th order explicit formula, called predictor, and then to refine yi+1 by a p-th order implicit formula, which is said to be the corrector. [Pg.269]

See also in sourсe #XX -- [ Pg.1021 ]

See also in sourсe #XX -- [ Pg.1126 ]

See also in sourсe #XX -- [ Pg.409 , Pg.415 ]

See also in sourсe #XX -- [ Pg.91 ]

See also in sourсe #XX -- [ Pg.1126 ]

** Adams-Moulton predictor-corrector method **

** Differential equations predictor-corrector method **

** Gear predictor corrector method **

** Gear predictor-corrector integration method **

** Potential predictor-corrector methods of molecular **

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