Are algebraic rules available outside simbiology?

I have reason to believe that the algebraic rules in simbiology could be of use to some simulations I am writing. I don't currently have the simbiology toolbox. Simbiology solves multiple differential equations. Therefore it strikes me that I should be able to write simlar rules for the ODE solvers. Would that be the case?

[Matthew Merritt]

Thanks, that was my impression. I have about 200 differential equations. Do you think it would be easier to use algebraic rules? Writing the DAE's looks like a place where I could make a lot of mistakes. Maybe I could send that to mupad?

Best regards

[Arthur Goldsipe]

I'm not sure I understand the question. I think writing DAEs to solve in ode15s is only slightly harder than writing ODEs to solve in ode15s. mupad might make things a little easier, but there are still probably a lot of ways to make a mistake.

If you're looking for a way to reduce the change of modeling errors in a biological kinetic model, then I suggest you take a look at getting a SimBiology license. You can construct the model in terms of reactions, and SimBiology will convert those reactions to the appropriate set of differential equations.

[Karan Gill]

DAEs are available in the Symbolic Math Toolbox, so you do not have to use MuPAD. See: http://www.mathworks.com/help/symbolic/set-up-your-dae-problem.html

Answer 1

[Arthur Goldsipe]

Hi,

Yes, you can include algebraic constraints with your differential equations when solving them in MATLAB using solvers like ode15s. These are called DAEs (differential-algebraic equations) as opposed to ODEs (ordinary differential equations). You indicate which terms are algebraic and which are differential using something called the mass matrix. You can find an example of this on the ode15s reference page. Just search the page for DAE, or look for the example named "Solve Robertson Problem as Semi-Explicit Differential Algebraic Equations (DAEs)."

-Arthur