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I have a surface difference that I have defined as an expression of x and t and can plot it, but I'm running into some trouble when I try to plot a 2d slice of the plot by itself on the line x = 0.25. I have tried to plot the 2d surface by defining a new function diff2d where I use With to set the value of x to 0.25, but this is not giving me any output for the plot.

What is a way to plot this line that I'm missing?

neq = 40;
sea[n_] := 2*Integrate[-Sin[n*Pi*x], {x, 0, 1}]
vn = Table[0, {n, 1, neq}];
Do[{vn[[n]] = sea[n] Sin[n*Pi*x] Exp[-(n*Pi)^2 * t]}, {n, 1, neq}]
vn;
v = Total[vn];
u = v + 1;
difference = u - Erfc[x/Sqrt[4 t]];
diff2d = With[{x = 0.25}, u - Erfc[x/Sqrt[4 t]]];
Plot3D[u, {x, 0, 1}, {t, 0, 1}, AxesLabel -> {"x", "t", "u"}]
Plot3D[Erfc[x/Sqrt[4 t]], {x, 0, 1}, {t, 0, 1}, 
 AxesLabel -> {"x", "t", "Erfc"}]
Plot3D[Evaluate[difference], {x, 0, 0.5}, {t, 0, 1}, 
 AxesLabel -> {"x", "t", "Difference"}]
Plot[Evaluate[diff2d], {t, 0, 1}, 
 AxesLabel -> {"t", "Difference on x = 0.25"}]
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  • $\begingroup$ MeshFunctions->(#1&),Mesh->{{0.25}} $\endgroup$
    – cvgmt
    Apr 8, 2021 at 2:10
  • $\begingroup$ Instead of With, how about a replacement: u - Erfc[x/Sqrt[4 t]] /. x->0.25. Or try Block[{x=0.25}, ...]. I think With only sets x when it appears directly within its body. $\endgroup$
    – tad
    Jan 3, 2022 at 18:57

1 Answer 1

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I found a hacky workaround, by using With[{x = 0.25}, Evaluate[diff2d]. I ran this part and copied the output of this new line into a plot statement. It has obvious disadvantages, like being wrong if I ever redefine my function without copying and pasting again, but works in a pinch.

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