Gear's predictor-corrector using Newton's equiations

graffy76

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Jul 17, 2008
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Hello,

I'm working on a little project that uses the Gear predictor-corrector numerical integrator on Newton's equations of motion. My problem is this:

Gear's predictor-corrector (in the case I am working with) is fifth-order. However, Newton's equations are third order. That means I need to come up with 1st and 2nd derivatives of acceleration in order to use Gear's. There is a force equation ( = dv/dt) that I'm using to describe the acceleration. It contains mostly vectors and scalars which are time dependent, but nothing is explicitly defined in terms of time.

This goes beyond the calculus I had in college, but I wonder if the problem is as difficult as I make it out to be. I would give some equations, but it takes more time than I have to type them out. If you're curious, you can view the document I'm basing this little experiment upon here:

http://public.rz.fh-wolfenbuettel.de/~apel/files/thesis.pdf

See pages 21-29 for more explicit information. The force equation for acceleration is summarized on page 26 and the predictor portion of Gear's integrator is on page 28. It's the predictor portion that's giving me the trouble.

The authors used Gear's as it's the most accurate integrator requiring the least computation. In this case it's important as the algorithm has n^2 complexity.

Any help is greatly appreciated.

Thanks.

Joel
 
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