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Calculating a product that is a function of NIntegrate?

Posted 2 months ago
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Hello everyone,

I am trying to calculate a Product, P1, that is a function of NIntegrate. This product is performed over j terms, where j is the number of elements in the list entitled Times1.

a = 3/100; b = d = 1; c = 1/2; k = HMax = 2000;

Times1 = {{100, 200}, {300, 400}};

System1 = ParametricNDSolve[{X'[t] == X[t]*b - a*X[t]^2/k,X[0] == Exp[-a*t0]*k},
{X}, {t, 0,1000}, {g, t0}]; 

 P1[g_, t0_?NumericQ] := Product[NIntegrate[ b*(1 - c*g)*(X[g, t0][t] /. System1)
/HMax - d,{t, Indexed[Indexed[Times1, j], 1],
1000},Method -> {Automatic, "SymbolicProcessing" -> 0}],
{j, 1, Length[Times1]}]

P1[0.6, 80]

When I try this, I receive an error stating that “t = Indexed[{{100.,200.},{300.,400.}},{j,1}] is not a valid limit of integration.” Is there a way to avoid this error? Any help would be greatly appreciated!

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POSTED BY: Alex L
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