Re: oscillations when solving nonlinear system


> Hi Andreas,
>
> with the implicit Euler method used, your system
> looks like
>
> 0=a*(phi_(j)-phi_(j-1))/deltaz + b*(phi_(j)-psi_(j))=
> F1(phi_(j),psi_(j))
>
> 0=c*(phi_(j)-psi_(j))+omega(psi_(j))=F2(phi_(j),psi_(j))
>
> This system of equations can be solved by Newton's
> method.
> To derive the corresponding Jacobian matrix in the step
> from z_(j-1) to z_(j) = z_(j-1) + deltaz,
> you have to compute dF1/dphi_(j), dF1/dpsi_(j),
> dF2/dphi_(j), dF2/dpsi_(j).
> The solution at z_(j-1) is known and thus constant
> in the equations.
>
> But the critical point with this simple method is
> that one uses a fixed step size in z-direction (despite possible large gradients of the species near the surface
> where step size should be chosen very small) and
> that the order of the Euler method is only 1.
> These shortcomings can be overcome by using an
> automatic DAE-integrator with adaptive
> z-stepping according to the locally estimated
> error of integration, as I would
> still advise you to do (and for which no
> Jacobian matrices need to be supplied :-) )
>
> Best wishes
> Torsten.


Well, cradau doesn´t work on my machine. Something goes wrong when I build
the library. I try the sundials package. I think I have to use the ida
package (which is made for DAE). I have to provide the functional vector
F. I have a 40 point grid in z-space and 8 Species. So the vector is
39x8x2 elemtents long. Is it better to solve the system for all points
together or only point by point in z-direction, which would last into a
8x2 system for every point.

Andreas



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