Can anyone shed some light on how matlab's bvp4c function works? I've looked online but I haven't found any specifics on the method it uses.
With that question asked, what are some different ways on solving bvp problems. I am aware of the shooting method, but for my problem I know exactly what my initial and end conditions are, I'm more interested in what happens in between. And unless I understand the method wrong, the goal is to figure out what your initial conditions are with the shooting method.
For my particular problem "4th order, non-linear, variable coefficient, homogeneous ODE. And by 4th order, I'm referring to the highest derivative" I'm having trouble figuring out a way to solve this problem.
Any help useful information would be greatly appreciated.
bvp4c
is a finite difference code that implements the three-stage Lobatto IIIa formula. This is a collocation formula and the collocation polynomial provides a $C^1$-continuous solution that is fourth-order accurate uniformly in $[a,b]$. Mesh selection and error control are based on the residual of the continuous solution. $\endgroup$