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Try option , MaxStepSize -> {.1, .01}


Interesting. OP has hit on an undocumented syntax of NDSolve that seems never be discussed in this site. As we can see, OP has typed {r, 0, ri, ri/50} inside NDSolve. This syntax isn't mentioned in the document AFAIK, and is colored red at least in the notebook of v8 and v9, but surprisingly, NDSolve still gives an output: T2 = 1000; ri = 0.001; inner = 0; ...


Here's a little addition related to the performance of NumericalFunction. Suppose we have a function like func = Cos[x + y^2] Sin[x^2 - y]; A NumericalFunction may be created as follows. The first variant nf0[{x0, y0}] returns a scalar. The second variant nf1[{x0, y0}] returns a 1-vector {z0} for a given input {x0, y0}, and the reason for including it will ...


To start the discussion on my own question... My basic understanding (or "what I think I understand") of these functions so far is as follows... Function 1: TemplateEvaluate: Causes the contents of its argument to be evaluated at the time TemplateApply is invoked, whether or not those contents are wrapped inside some function that has HoldFirst, ...

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