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I am working on a personal project that models the movement of pedestrians in large crowds. I am using something called the "social force model" and came across a master's thesis which describes an improved implementation. The model constructs a very large force equation to model the way people try to avoid each other / stationary objects as they navigate busy areas. In this case, a very large force equation to describe the acceleration of each pedestrian is developed (F=ma, assuming unit mass).

As I read the thesis, the authors described that they implemented the model using Gear's predictor/corrector to do the integration. The problem is that the Gear method requires first and second derivatives of the force equation (dV/dt), yet the equation itself is not explicitly described in terms of time.

I'm rusty on my phyics / diff eq's, so I suspect this is simpler than it appears to me. The thesis can be found at:

http://public.rz.fh-wolfenbuettel.de/~apel/files/thesis.pdf" [Broken]

The model is described on pages 21-26 and the Gear implementation is on 28 and 29.

Again, this can't be as hard as it appears to me. Any suggestions?

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# Gear predictor / corrector

Can you offer guidance or do you also need help?

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