NDSolve: Reinitialize fails with If condition

Question

I have found a weird problem using If conditions containing an state inequality of the form state<=.

First consider the simple ODE with an If condition t<=2. We first process the equations.

state = First@NDSolve`ProcessEquations[{r'[t] == If[t <= 2, 2, 0], r[0] == 0},r, t]
NDSolve`StateData[SequenceForm["<", 0., ">"]]

Then we reinitialize the system by

newstate = NDSolve`Reinitialize[state, {r[0] == 1}]
NDSolve`StateData[SequenceForm["<", 0., ">"]]

which works absolutely fine. Now consider another ODE system with a slightly different If condition, namely If[r[t] <= 2, 2, 0]. We process the equations with

state2 = First@NDSolve`ProcessEquations[{r'[t] == If[r[t] <= 2, 2, 0], r[0] == 0},r, t]
NDSolve`StateData[SequenceForm["<", 0., ">"]]

which works fine. Now when we try to reinitialize this system we get an error message!

newstate2 = NDSolve`Reinitialize[state2, {r[0] == 1}]
NDSolve`Reinitialize::ntcs: Cannot solve constraint equations for initial conditions.

It seems like when I try to reinitialize Mathematica has a problem due to the condition r[t]<=2. I have noticed the same problem with for example PieceWise functions, as noted in this post:

NDSolve: ProcessEquations and Reinitialize with Piecewise functions

Answer 1

I filed this as a bug. Here is a workaround. It's much easier to use ParametricNDSolve for this:

pf = ParametricNDSolveValue[{r'[t] == If[r[t] <= 2, 2, 0], r[0] == a},
   r, t, a]

pf[0]
pf[1]

As an alternative, you could try to experiment with:

g[in_?NumericQ] := If[in <= 2, 2, 0]
state2 = First@
   NDSolve`ProcessEquations[{r'[t] == g[r[t]], r[0] == 0}, r, t];
newstate2 = NDSolve`Reinitialize[state2, {r[0] == 1}]

Hope that helps.