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Mathematics
General Math
How can you know if a numerical solution is correct?
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[QUOTE="m4r35n357, post: 6061338, member: 397175"] The main method I currently use is to compare my answer with a "better" solution (example search term "Clean Numerical Simulation"). It sounds a bit obvious, but if you do another simulation with higher precision/order and smaller timestep, you can compare the results and see where they are diverging. This can be automated. I use arbitrary precision (MPFR) arithmetic for mitigating roundoff and because I trust INRIA more than I trust Intel to do floating point properly ;) I use the Taylor Series Method to obtain arbitrary order of integration. Sometimes there are invariants and constants that you can evaluate and monitor. There are always local error estimates, but I tend to solve nonlinear ODEs that get rather degenerate or chaotic and these render local error irrelevant. [/QUOTE]
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How can you know if a numerical solution is correct?
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