# [petsc-users] KSPBuildSolution

Juha Jäykkä juhaj at iki.fi
Mon Feb 21 06:10:19 CST 2011

```> > introduce new variables to reduce the problem to a first order equation.
> > For example let g = f'  and the new problem is F(f,g,g') = 0 with the
> > additional equations g = f' now there are no second derivatives.
> Let me see what happens if I do that...

Ok, so this helps. Now I can get the solution to converge on a small lattice,
of less than 20 points.

Increasing the lattice gives divergent zig-zag "solutions". Now this is usual
central differences behaviour: it decouples even lattice points from odd ones
and now that I have both f and f' as unknowns, this decoupling is total. (It
was not previously, since f'', computed from f, does not decouple.)

Changing to simple forward differences does not help, but changing to three-
point forward differences (=five-point stencil, but the backwards points are
not used) fixes the problem and I now get convergence.

That is, thanks for all the help. I can now return to my actual equation,
which still does not converge with these tricks on any lattice larger than
about 50 points. I suppose the problem here is similar and I just need to find
a better discretisation.

Cheers,
Juha

--
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| Juha Jäykkä, juhaj at iki.fi			|
| http://www.maths.leeds.ac.uk/~juhaj		|
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