I am dealing with a large system of nonlinear equations and I am having trouble computing its zeros numerically because it is very stiff. Can you suggest approaches to deal with this? Perhaps some transformation of the variables?
Thank you very much for your help!
If its a differential equation, you can use trapezoidal method (Adams-Moulton method).
Thank you for your input. I see this method may work to solve a stiff system but it does not generate a new equivalent system that is less stiff, which is what I would like to achieve. Is there any way to do this?
Well, I think that appearence of stiffness is a response of the physics of a problem where different characteristic scales appear. You can think about a proper numerical methodology to integrate the equations. Have a look here fore example
https://www.springer.com/us/book/9783540604525
Vincent, I do not know your specific application(s). But for instability studies of external flows, we have used compound matrix method with success. Essentially it removes the stiffness of the problem, in the re-cast equations involving second compounds, and which can then be solved by any standard solvers. A qualifier to this suggestion: I am talking about solving stiff ordinary differential equations only.
Thank you all for your answers and particularly Prof. Sengupta. The compound matrix method seems very powerful but very laborious to develop: I have only seen it applied to specific flow equations. Do you know of any reference in which it is applied to other types of equations?
My knowledge is based on personal experience with boundary layers with and without heat addition. You can see the references of Prof. Tom Bridges, he is the most knowledgeable about compound matrix method on the mathematics side. Also, take a look at the book by Boris and Oran on CFD, where there is some discussion on stiff differential equation related to chemical kinetics. Hope this helps.
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