Hello,

My neverending efforts to force NDSolve to very accurately solve a certain PDE have led me to try to solve a corresponding system of nonlinear ODEs resulting from orthogonal collocation discretization. I finally managed to obtain a reasonably looking solution of this system by using NDSolve with default settings, but I would prefer to use fixed grid implicit Runge Kutta methods, because I want to study convergence by varying step sizes. I also see (by considering some other, simpler examples) that fixed grid RK methods tend to produce more accurate results, whereas the default automatic solver yields solutions that sometimes have errors much bigger than assumed tolerances. Unfortunately, in the fixed grid case I get an error message:

NDSolve::ndcf: Repeated convergence test failure. Unable to continue.

and the calculations are interrupted. What this message means and is there any way to avoid it? For me this message is incomprehensible, because in the case of fixed grids I don't see a reason for any convergence tests. I would rather expect them in the case of default NDSolve settings, as in such a case some automatism is involved.

Lesław