ode15s and 0de23 very slow at high frequencies

Hi all!

I have a SDOF mass + non-linear spring system excited by a sine wave. I am solving for the displacement of the system by using ode15s for a range of excitation frequency between 200:0.1:300. ode15s runs very slowly, and when I try using ode23 is goes even slower.

Is this always the case for higher frequencies or should I pay attention to the setting of some parameters to speed up the process?

Thank you!

Answer 1

[Torsten]

I have no experience with the physical background, but if for low frequencies, the solution somehow looks like sin(0.001*x) and for high frequencies somehow like sin(1000*x), you can easily see from the graphs that for high frequencies, much smaller time steps are needed to resolve the solution than for low frequencies. In other words: there are no solver options that can speed up the calculations for high frequencies if you want to keep accuracy constant.

[Jan]

The simulation of fast vibrations can be accelerated, if the model does not use the cartesian x and y coordinates, but e.g. the angle. E.g. integrating wheel rotating with a static speed is expensive with cartesian coordinates, while the integration of the rotational angle is very cheap: alpha * t.

Answer 2

[Jan]

Are you sure that the problem is stiff? If not, use ODE45 instead of the stiff solvers.

The relative and absolute tolerances influence the processing speed significantly.