Best ODE solver when there is a parameter discontinuity
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Hello,
I have a system of differential equations where one of the parameters changes value abruptly at one point in time. Which ODE solver is the most accurate and most efficient to use in such a situation? I'm trying to use ode45, but when I use a low tolerance, I'm not getting an accurate answer. When I try to tighten, the tolerance, it is taking an extremely long time to run (it's been running over an hour and still hasn't finished).
Thank you, Kevin
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Jan
2013-8-15
Matlab's integrators cannot handle discontinuities reliably, see e.g. http://www.mathworks.com/matlabcentral/answers/59582#answer_72047. The correct method is to stop the integration at the time point of the change and restart it. Then you can choose the integrator according to the numerical properties of the ODE, most of all its stiffness.
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Jan
2013-8-17
The description of the problem is too vague to understand it in detail. Does your function to be integrated depend on a discontinuos parameter? What exactly does "different values at each time point" mean? This would match the parameter "t" also.
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