Solve from the differential equation below numerically for the function [itex] \phi(x) [/itex] for [itex] x \in [0,L] [/itex]
[tex]\phi '' (x) + D(x) sin(\phi (x) ) + E sin(\phi (x) ) cos( \phi (x) ) = 0 [/tex]
with D(x) a polynomial.
The Attempt at a Solution
I can rewrite it in a state space form and then iterate towards the function [itex] \phi(x) [/itex] if D is constant. But what can I do with that pesky D(x). If I am iterating towards D(x) I cannot iterate, right?