Differential Equation 1.4

# Differential Equation 1.4 - Predictor-corrector algorithms...

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¾ Predictor. From the positions and their time derivatives up to a certain order (all at time t) one “predicts” the same quantities at time t + h using the Taylor expansion. ¾ Force calculation. The force acting on a given particle is computed for the predicted positions. The acceleration a = F/m will be in general different from the “predicted acceleration”. The difference between the two constitutes the “error signal”. ¾ Corrector. The error signal is used to correct the positions and their derivatives. All the corrections are proportional to the error signal. The coefficients of proportionality are “magic numbers” chosen to maximize the stability of the algorithm. Another commonly used class of methods to integrate equations of motion are predictor-corrector algorithms. These methods can be used in simulations with velocity-dependent forces, such as in constant-temperature MD methods that will be discussed later in this course. Predictor-corrector algorithms

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## This note was uploaded on 02/14/2012 for the course MSE 4270 taught by Professor Zhigilei during the Fall '11 term at UVA.

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Differential Equation 1.4 - Predictor-corrector algorithms...

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