Hi,

i need to find the final value(s) of a linear first-order ODE system to display the effect of different parameter values on the steady-state response. There are at the moment 6 differential equations with more then ten parameter. At the moment I have a working solution, however with increasing number of parameter and complexity (nonlinear terms), the calculations take longer and longer. So I was wondering, if anybody can suggest me a faster/better approach?

What I do now is (see also attached notebook):

• write down the ODE system in the time domain
• apply LaplaceTransform[] to the equation system
• solve for all dependent variables
• determine the final value by applying the final value theorem
• plot the resulting functions in Manipulate[] (here the ODE parameter get numerical values for the first time)

That process can take 15minutes or more to calculate (its much faster in the simplified and attached example). That makes me think that this is not a good solution...

I have seen that there is also the function DSolve, which can take the ODE system in the time domain. When I applied this function to my equation system it just kept calculating. -So not sure if this is the right way.

Would be great if somebody could give me some advice on how to find the final values in an efficient way.

Thanks!

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