# Update NumericalFunction in NDSolve

I have NDSolve StateData from an NDSolve ProcessEquations evaluation. I can NDSolve Iterate from t0 to t1, but then my boundary condition (an interpolation function) runs out of data.

This interpolation function gets updated externally. I just want to continue iterating (t1 to t2) with the updated interpolation function. However, calling myStateData@"NumericalFunction" shows that NDSolve holds onto the old interpolation function, even though this function is defined with a delayed set i.e. myInterpFunction[t_]:=something[t]

Is there any way to update the functions inside of the state data?

Here is a simplified version of what I'm doing:

myStateData = NDSolveProcessEquations[
{myPDE[x,t],
(*boundary conditions*)
T[xf, t] == myInterpolationFunction[t],
T[0, t] == 0,
(*Initial condition*)
T[x, t0] == initialCondition[x]};
T, t, {x, 0, xf}]


Then I need to solve so...

NDSolveIterate[myStateData,t1]


Then externally I update my boundary condition so that now it goes to t2 but when I evaluate

NDSolveIterate[myStateData,t2]


Mathematica returns an error saying that the interpolation function doesn't cover that range (t1 - t2) because it's holding onto the old interpolating function. In other words, looking at

myStateData@"NumericalFunction"


shows myInterpolationFunction has a domain of {t0,t1}

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• Please include your actual code, or a simplified version of it if practical, so that readers can understand what you are doing. – bbgodfrey Apr 12 '15 at 19:43
• I've added simplified code. My interpolation function is good from "t0" to "t1", once I update the function to go to "t2" I need NDSolve to continue Iterating/integrating to t2 – Eric William Smith Apr 12 '15 at 19:51
• Try myInterpolationFunction[t_?NumericQ] := something[t]. See also mathematica.stackexchange.com/questions/18393/… – Michael E2 Apr 12 '15 at 21:12
• (If you did try it and it did not work, then I suggest it is because the problem is not sufficiently described in the question. There must be something in the missing details that causes an unanticipated problem.) – Michael E2 Apr 13 '15 at 2:10