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I am trying to use ParametricNDSolve to solve a set of ODEs, but I want to give a range for the parameter before solving the equations. How can I constrain the range of the parameter that ParametricNDSolve should use?
For example, in the equation below, I want to try and solve the ODEs for a between 4 and 6 only.
ParametricNDSolve[{y'[t] == a y[t], y[0] == 1}, y, {t, 0, 10}, {a}]
Your question seems to raise a non-issue. The parametric function returned from evaluating
yF = ParametricNDSolveValue[{y'[t] == a y[t], y[0] == 1}, y, {t, 0, 10}, {a}]
is good for any value of a in your range of interest. This is demonstrated by
LogPlot[Evaluate @ Table[yF[a][t], {a, 4, 6, .5}], {t, 0, 10}, PlotRange -> All]
If, for further calculations, you have the need to constrain evaluation to a in the stated range, you can derive a constrained family of functions like so:
yCF[a_ /; 4 <= a <= 6] := YF[a]
yCF will only accept parameter values in stated range and return unevaluated for any other values.
d = {{9.721036901*10^-7, 0.80119823*10^-6}, {9.728704323*10^-7, 0.83015194*10^-6}, {9.728577185000001*10^-7, 0.857031534*10^-6},{9.728430487000002*10^-7, 0.88804645*10^-6}, {9.733506242*10^-7, 0.914930348*10^-6}, {9.733359543*10^-7, 0.945945264*10^-6}}; b = Interpolation[d, InterpolationOrder -> 1]; bb = b[a]*10^-4; yF = ParametricNDSolveValue[{y'[t] == bb y[t], y[0] == 1}, y, {t, 0, 10}, {a}], Mathematica is solving the DE but Ican't plot anything.
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Jan 10, 2017 at 22:37
sol = y /. ParametricNDSolve[....]you can justsol[4]to havea=4and also for otherathat you're interested in. $\endgroup$