Best ODE solver when there is a parameter discontinuity

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Kevin Bachovchin 2013-8-14

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https://ww2.mathworks.cn/matlabcentral/answers/84749-best-ode-solver-when-there-is-a-parameter-discontinuity

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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Answer 1

Jan 2013-8-15

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https://ww2.mathworks.cn/matlabcentral/answers/84749-best-ode-solver-when-there-is-a-parameter-discontinuity#answer_94392

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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Kevin Bachovchin 2013-8-16

Thanks for your response. I tried what you suggested. Now the first call to ode45 runs fine, but the second call to ode45 runs for a very long time without finishing (or if use a loose tolerance is inaccurate). In the second call to ode45, after the parameter disturbance, I have a controllable variable (which is an algebraic function of the state variables) which takes different values at each point in time. I think this might be what is causing the problem. Do you have any suggestions for dealing with this issue?

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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