how do i choose a solver?

[Ranjit Chacko]

Hi,

I've got an equation of the following form:
localTerm = -6.0*self.phi**5 + 8.0*self.phi**3 - 2.0*self.phi*self.tau
(TransientTerm() == DiffusionTerm(coeff=0.5 * self.a) +  
DiffusionTerm(coeff=(0.25 * self.b, 1.0)) + localTerm)

I get very different behavior depending on which solver and how many  
iterations I choose. Are there any rules of thumb about how to choose  
a solver and are there any good references about these methods I  
should look up?

Thanks,

-Ranjit