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2

Some of the definitions in the original question were problematic. I edited the question to have more consistent code. In order to plot the function numerical values are needed, so using Integrate is not necessary. We can use NIntegrate instead. The plot is produced within 30 seconds on my laptop with Mathematica 10.3.1. Here is the function redefined: ...


0

intDawson[i_Interval] := Module[{peak, xpeak}, {peak, xpeak} = {NMaxValue[DawsonF[x], x], NArgMax[DawsonF[x], x]}; Interval[ If[IntervalMemberQ[i, xpeak], {#[[1]], peak}, #] &@ If[IntervalMemberQ[i, -xpeak], {-peak, #[[2]]}, #] &@ Sort[DawsonF @@ i // N]] ] intDawson[Interval[{-10, 10}]] (* Interval[{-0.541044, 0.541044}] *) ...


0

It is best practice to avoid upper-case letters (such as your F) to start the names of variables and functions. I suspect your problem was that your F had been defined elsewhere during your Mathematica session. Without such a pre-definition, DiracDelta works fine in two dimensions: Integrate[ DiracDelta[x, y] f[x, y], {x, -\[Infinity], \[Infinity]}, ...


3

Just a comment-with-visuals here. The problem is evaluating that ParabolicCylinderD function. My thinking is always that you should be able to evaluate a function reliably before you try to plot it. Also, that plot takes forever to evaluate, so I hate to do it and have garbage come back. So my workflow would be to evaluate the function at a set of ...


3

More insight can be obtained by defining f[x_?NumericQ] := Sow[Re[N[y[x, 20], 30]]] and computing Reap[DiscretePlot[f[x], {x, -Pi, Pi, Pi/50}, WorkingPrecision -> 30]] (Only 101 points are computed to save time.), which returns a plot similar to the first one in the question and a List of 101 values, each of precision near 30. On the other hand, ...


5

c = 0.01333 // Rationalize; Ang[x_] = -I Log[-Exp[I x]]/2; y[x_, t_] = FullSimplify[ DSolveValue[{ u''[t] + (4 (c t - Cos[x])^2 + 4 Sin[x]^2 + I 2 c) u[t] == 0, u'[0] == I 2 Cos[x] Cos[Ang[x]] - I 2 Sin[x] Sin[Ang[x]], u[0] == Cos[Ang[x]]}, u[t], t], {Element[t, Reals], -Pi <= x <= Pi}]; The above definition is in terms of ...


8

As march predicted in a comment above, the noise in the plots is a precision issue. A small improvement can be obtained by setting c to a rational number, c = 4/300 and applying FullSimplify to y[x, t]. before plotting. Nonetheless, even at t = 0, the solution is quite noisy. To illustrate, compare the initial condition on u with y[x, 0]. p0 = ...


2

A partial answer using the reference that you provided: Limit[b^-1 MeijerG[{{0}, {}}, {{0}, {}}, x^(-5/2)/b], b -> 0] (* x^(5/2) *) Assuming[{x >= 0}, Sqrt[π] MeijerG[{{}, {}}, {{1/2}, {0}}, 4 x^2] // Simplify] (* Sin[4 x] *)



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