Dear Wolfram Community,
I have a formula, and would like to visualize it. The formula consists of two consecutive integrations. I defined my formula with embedded Integrate commands in Wolfram Mathematica, but I got numerous error messages. I also tried with NIntegrate command, with the "?NumericQ" hint, but nothing changed.
Here is my code with the error messages:
Clear["Global`*"]
(*$MaxExtraPrecision=50*)
In[212]:= Integrate[
Integrate[
G1[t - \[Gamma][x, k] - T]/(T*Sqrt[k*(1 - k)]), {T, -\[Beta][x, k],
t - \[Gamma][x, k]}], {k, 0, 1}]
Out[212]= \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(1\)]\(\((
\*SubsuperscriptBox[\(\[Integral]\), \(-\[Beta][x,
k]\), \(t - \[Gamma][x, k]\)]
\*FractionBox[\(G1[t - T - \[Gamma][x, k]]\), \(
\*SqrtBox[\(\((1 -
k)\)\ k\)]\ T\)] \[DifferentialD]T)\) \[DifferentialD]k\)\)
cons1 = -1/Sqrt[33];
cons2 = 808/(99*Sqrt[33]);
cons3 = 128/(99*Sqrt[33]);
cons4 = 2/Sqrt[33];
In[217]:= \[Gamma][x_, k_] =
cons1*(1 - 2*k)*x + cons2*k + cons3*Log[k/(1 - k)];
\[Beta][x_, k_] = (cons4*x + cons2)*k;
In[219]:= G1[t_] = Exp[-(t)^2];
In[220]:=
u[t_, x_] =
Integrate[
Integrate[
G1[t - \[Gamma][x, k] - T]/(T*Sqrt[k*(1 - k)]), {T, -\[Beta][x, k],
t - \[Gamma][x, k]}], {k, 0, 1}];
In[221]:= Plot[u[0, x], {x, -10, 10}, PlotRange -> Automatic]
During evaluation of In[221]:= NIntegrate::inumr: The integrand \!\(\*SubsuperscriptBox[\(\[Integral]\), \(2.0606558625765237`\ k\), \(\(-1.7407054364004024`\)\ \((1 - 2\ k)\) - \*FractionBox[\(808\ k\), \(99\ \*SqrtBox[\(33\)]\)] - \*FractionBox[\(128\ Log[\*FractionBox[\(k\), \(Plus[<<2>>]\)]]\), \(99\ \*SqrtBox[\(33\)]\)]\)]\(\*FractionBox[SuperscriptBox[\(E\), \(-\*SuperscriptBox[\((<<1>>)\), \(2\)]\)], \(\*SqrtBox[\(\((1 - k)\)\ k\)]\ T\)] \[DifferentialD]T\)\) has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,1}}. >>
During evaluation of In[221]:= NIntegrate::inumr: The integrand \!\(\*SubsuperscriptBox[\(\[Integral]\), \(2.0606558625765237`\ k\), \(\(-1.7407054364004024`\)\ \((1 - 2\ k)\) - \*FractionBox[\(808\ k\), \(99\ \*SqrtBox[\(33\)]\)] - \*FractionBox[\(128\ Log[\*FractionBox[\(k\), \(Plus[<<2>>]\)]]\), \(99\ \*SqrtBox[\(33\)]\)]\)]\(\*FractionBox[SuperscriptBox[\(E\), \(-\*SuperscriptBox[\((<<1>>)\), \(2\)]\)], \(\*SqrtBox[\(\((1 - k)\)\ k\)]\ T\)] \[DifferentialD]T\)\) has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,1}}. >>
During evaluation of In[221]:= NIntegrate::nlim: T = 2.06066 k is not a valid limit of integration. >>
During evaluation of In[221]:= NIntegrate::nlim: T = 2.06066 k is not a valid limit of integration. >>
During evaluation of In[221]:= NIntegrate::nlim: T = 2.06066 k is not a valid limit of integration. >>
During evaluation of In[221]:= General::stop: Further output of NIntegrate::nlim will be suppressed during this calculation. >>
During evaluation of In[221]:= NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
During evaluation of In[221]:= NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 9 recursive bisections in k near {k} = {0.977018969826617}. NIntegrate obtained 3.209851121191303` and 3.2931163356283615` for the integral and error estimates. >>
Out[221]= $Aborted
Could somebody point me out the right direction or suggest a hint? Any help is appreciated.
