Integration procedures predictor-corrector

A predictor-corrector algorithm for automatic computer-assisted integration of stiff ordinary differential equations. This procedure carries the name of its originator. ... 

It was noted earlier that the choice of integration algorithm will depend partially on the mode of operation of the computer center. We would like now to illustrate the role that this factor might play in a decision between the predictor-corrector and the Runge-Kutta-Gill procedures. 

Few-body problems can be handled by conventional integrators, such as Runge-Kutta or Adams-Moulton methods. Here one calculates the position and velocity for each particle and then the precise two-body interaction for that body with every other particle in the system. Both methods are predictor-corrector procedures in which the next step is computed and corrected iteratively. Leapfrog methods, which use the velocity from one step and the positions from the previous step to compute the new positions, are also computationally efficient and stable. The basic problem is to solve the equations of motion for a particle at position Fj,... 

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