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Does NDSolve step size for coupled ODEs get bottlenecked by stiffest one?

Posted 6 months ago

I have a system that looks like dF/dt= sigma \gradient F, where F is a vector quantity. There are big differences in the components of the gradient (at least away from equilibrium, where the gradient=0), and I think the largest component needs a small step size, which unfortunately makes ALL the equations have a small step size. I would like to first know if this is true: if the method used in NDSolve does indeed do this, and if so (since for now I only care about finding the equilibrium), is there a way to make sigma a vector too, so that its (adaptive) magnitude is inversely proportional to the relative component of the gradient? This would need to be done inside NDSolve somehow?

POSTED BY: Iuval Clejan
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