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Originally Posted by flameout
If I really cared about accuracy and speed, I would be using Simpson's Rule integration...
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It's a cost/benefit thing. The cost of converting Euler to trapezoidal for this problem is very small. Going from trap to Simpson's would require more rework, make the code less readable, and probably even slow it down for equivalent accuracy.
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Another good technique would be to use an ODE solver rather than pure integration -- if I were to do this, I'd probably use MATLAB's built in 4th/5th order adaptive Runge-Kutta solver (ode45). This would probably be plenty fast as well.
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It would be interesting to do a comparison. My guess is that for this problem, trapezoidal in compiled C would be just as fast for equivalent accuracy as RK in MatLab.