NDSolve`ImplicitRungeKuttaGaussCoefficients doesn't work

Question

I am using Mathematica 9.0 on Ubuntu.

I tried the first example from this documentation page, but it returns unevaluated:

Needs["DifferentialEquations`NDSolveProblems`"];
Needs["DifferentialEquations`NDSolveUtilities`"];

NDSolve`ImplicitRungeKuttaGaussCoefficients[4, 50]

(* ==> NDSolve`ImplicitRungeKuttaGaussCoefficients[4, 50] *)

What is the problem ?

Answer 1

This example works in version 8, but in version 9 it does indeed fail to evaluate.

I did a little bit of spelunking to find out why. It turns out that in version 9 this function (as well as related ones) takes a third argument. I believe this third argument is just a symbol that will be used as the head in any messages that might be reported. Maybe this change was done because version 9 has four different NDSolve-related functions (compared to v8): NDSolve, NDSolveVaule, ParametricNDSolve and ParametricNDSolveValue.

The simple workaround is to just pass NDSolve as the third argument:

NDSolve`ImplicitRungeKuttaGaussCoefficients[4, Infinity, NDSolve]

(* ==> {{{1/4, 1/12 (3 - 2 Sqrt[3])}, {1/12 (3 + 2 Sqrt[3]), 1/4}}, {1/2, 1/2}, {1/6 (3 - Sqrt[3]), 1/6 (3 + Sqrt[3])}} *)