How to choose a numerical method?

Hi,

i am solving a "duffing-like" 2nd order nonlinear diff. equation (in Matlab)
using Dormand-Prince method (based on an explicit Runge-Kutta (4,5) formula)
with variable step. However, how can i be sure that i have chosen a "good
method", i.e. how can i examine the method, i.e. the errors of method used
for solving of my equation?

Please, help!

Thanks.


P.S. I posted this question on math-group and matlab-group also, but then it
was recommended to me that i should send it to this group. So, sorry for
spaming :-/


.

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