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Unformatted text preview: N S E M I Now we know how to define the t and how to make the neighbour check. I So, we can concentrate on solving the equations of motion (assuming we know f i ( r ) ). I Finite difference methods are a group of methods which aim at solving differential equations by small increments to the initial values. I In the case of MD, this means using the positions r ( t ) and velocities v ( t ) to solve the state of the system at a later time r ( t + t ) , v ( t + t ) . I This discussion follows mostly the correponding chapter in Allen and Tildeslay a a Allen and Tildeslay, Computer Simulation of Liquids , Oxford University Press (1987) Notes I An example of finite difference methods is the predictor corrector algorithm in which the Taylors expansion is used to predict the new state of the system, e.g. r p ( t + t ) = r ( t ) + t v ( t ) + 1 2 t 2 a ( t ) + 1 6 t 3 b ( t ) + . . ....
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This note was uploaded on 02/14/2012 for the course CSE 6590 taught by Professor Kotakoski during the Winter '12 term at York University.
- Winter '12