Create a reverse function of Numeric function result from NDSolve

Questions
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1

Hi There
I’m pretty new to Mathematica.
I have numeric function that is a result of solution of ODE equation from NDSolve. (H as function of R) I’m trying to get the reverse reciprocal function R as function of H in order to solve this equation:
DH/dt=R[H]/6-2*H^2 in order to get H as function of t.
When I tried the Inverse function, it expected to get a square matrix, but I’m not sure how to go around it?
Thank u. Ezra

R power of 2.nb (44 KB)

2

Hi Ezra,

You need to use InverseFunction, not Inverse.

TT = InverseFunction[S1];
Plot[TT[x], {x, Splice[S1 @@ S1["Domain"]]}]

6176plot.png
6176plot.png360×224 5.76 KB

3

Thank u Rohit. It worked. I do have another basic question for u:
I would like to solve this equation dx/dt=TT/6-2*x^2 after I found the inverse function so now TT is a function of x with domain 0,700. I’m going to use to solve it by using the integrate function.

T = Integrate[1/(TT/6-2*x^2), x] which worked.
and then inverse again to get x function of t by using t = InverseFunction[T].
but plotting of the t does not show anything.
Ezra