How to deal with very small and very large parameter values while solving DAE?

I have to solve a system of differential algebraic equations wherein some of the parameter values are very large (e.g. of the order of 10^5 to 10^10) and some other parameter values are very small (e.g. order of 10^-4 to 10^-6). I use ode15s, but the code breaks saying:

Warning: Failure at t=1.000000e-03.  Unable to meet integration tolerances without reducing the step size below the smallest value allowed
(3.552714e-18) at time t.

How do I resolve this?

[Torsten]

And you are sure the code fails because of the mentionned scaling problem ? It's impossible to give advice without seeing your DAE system.

[Monisha S R]

Yes, I think the code fails because of the scaling problem, because it works for certain other parameter values. I have attached my problem in an image file (it's rather a huge problem). I have discretised in the spatial coordinate \zeta and then fed into the matlab function file. Here, k2,k3 and k4 are the large parameters and Dc, Dh are the small parameters.

[Torsten]

Since the code stops right at the beginning of the integration, I doubt that it's a matter of scaling. Did you check the time derivatives for NaN or Inf values ?

[Monisha S R]

@Torsten I haven't checked the time derivatives for NaN values. Will do. Thanks. :-)

[Monisha S R]

Hi David, I haven't looked at pdepe yet. Yes, I'm solving the system for a large vector of dependent variables after discretization in zeta. I don't understand the notation u and nu in your explanation. My equations are all non-dimensionalised.

[David Goodmanson]

Hi Monisha,

I made up names u and nu for new rescaled variables in place of t and zeta respectively. Having thought about it more, I don't think what I wrote in the previous comment is adequate, so I withdrew it.

[Monisha S R]

@Torsten How do I output time derivatives from the matlab function file?Thanks.

[Torsten]

When you generate the vector of time derivatives, just omit the semicolon at the end of the line.

[Monisha S R]

Hi Torsten, My vector is very long (like 4000 elements), so outputting to the command window and checking the values is a tedious process. But nevertheless I can try with a smaller number of nodes. Thanks.