I want to use NDSolve to solve a BVP using the shooting method. I want the integrator to be an implicit Runge Kutta Method different than the one provided by Mathematica. For explicit methods documentation shows how to provide the method coefficients. For Implicit integrators it does not. Does anyone has an idea how I can overcom the problem.
I guess that these coefficients are generated automatically and you can not use arbitary set of such numbers. If you want to customize them thru changing the order of the solver, there is a piece of article about the advanced adjustment you can use in the NDSolve.
If you want to check the result of your simulation, this link shows some handy examples of visualize how the local/global error varies as you update the methods and initial guess.