4
$\begingroup$

Consider the functions

\[Lambda][n_] := ((n \[Pi])/L)^2

\[ScriptCapitalX][
x_] := \[ScriptCapitalC][1] Cos[Sqrt[\[Lambda][n]] x]

\[ScriptCapitalT][t_] := 50 E^(-\[Lambda] t)

to give the Sum product solution

\[ScriptCapitalU][x_, 
t_, \[ScriptCapitalN]_] := \[ScriptCapitalX][x] \[ScriptCapitalT][t]

Notice that the 2D and 3D plot of the Sum product solution, respective are

Plot[Evaluate@
ReplaceAll[
Table[\[ScriptCapitalX][x] \[ScriptCapitalT][t], {n, 1, 3}, {L, 1, 
 1}], {\[ScriptCapitalC][1] -> 1, \[Lambda] -> 1, t -> 0}], {x, 0,
1}, PlotLegends -> "Expressions", AxesLabel -> {"x", "t"}, 
PlotLabel -> "2D Plot Behaviour for \[ScriptCapitalU](x,t)"]

and

Plot3D[ReplaceAll[
Table[\[ScriptCapitalU][x, t, \[ScriptCapitalN]], {n, 1, 3}, {L, 1, 
1}], {\[ScriptCapitalC][1] -> 1, \[Lambda] -> 1}], {t, 0, 1}, {x, 
0, 1}, AxesLabel -> Automatic, 
PlotLabel -> "3D Plot Behaviour for \[ScriptCapitalU](x,t)"]

If you rotate the 3D point such that the x and t plots points "towards" you, you are able to observe that they corresponds qualitatively to the 2D plot.

enter image description here enter image description here In the case of the 3D plot, how do I match the different colours to different "n" for n=1 to n=3?

Any help is appreciated.

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2
  • 1
    $\begingroup$ in Plot3D[...] add the options Evaluated->True or wrap the first argument with Evaluate as you did in Plot. $\endgroup$
    – kglr
    Commented Jan 22, 2018 at 8:10
  • $\begingroup$ @kglr It doesn't work $\endgroup$
    – Physkid
    Commented Jan 22, 2018 at 8:13

2 Answers 2

5
$\begingroup$
Plot3D[Evaluate@
  ReplaceAll[Table[\[ScriptCapitalU][x, t, \[ScriptCapitalN]], {n, 1, 3}, {L, 1, 1}], 
 {\[ScriptCapitalC][1] -> 1, λ -> 1}], {t, 0, 1}, {x, 0, 1}, 
  AxesLabel -> Automatic, 
  PlotLabel -> "3D Plot Behaviour for \[ScriptCapitalU](x,t)"]

enter image description here

Note: Interestingly, the combination of options Evaluated ->True + PlotStyle -> {Red, Green, Blue}, which works in version 9, does not work in version 11.2 (on Wolfram Cloud).

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1
  • $\begingroup$ my code bellow works in version 11.2 (PC client). $\endgroup$
    – PureLine
    Commented Jan 23, 2018 at 7:34
4
$\begingroup$
\[Lambda][n_] := ((n \[Pi])/L)^2
\[ScriptCapitalX][x_] := \[ScriptCapitalC][1] Cos[Sqrt[\[Lambda][n]] x]
\[ScriptCapitalT][t_] := 50 E^(-\[Lambda] t)
\[ScriptCapitalU][x_, t_, \[ScriptCapitalN]_] := \[ScriptCapitalX][x] \[ScriptCapitalT][t]

Plot3D[Evaluate@ (* Step 2: enforce the evaluation before configuring the colors *)
  ReplaceAll[Table[\[ScriptCapitalU][x, t, \[ScriptCapitalN]], {n, 1, 3}, {L, 1, 1}], {\[ScriptCapitalC][1] -> 1, \[Lambda] -> 1}], {t, 0, 1}, {x, 0, 1}, 
  AxesLabel -> Automatic, PlotLabel -> "3D Plot Behaviour for \[ScriptCapitalU](x,t)",
  PlotStyle -> {Red, Green, Blue}] (* Step 1: use PlotStyle to set up color for each plot surface *)

enter image description here

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3
  • $\begingroup$ how is this different from the earlier answer below?:) $\endgroup$
    – kglr
    Commented Jan 22, 2018 at 8:24
  • $\begingroup$ @kglr maybe we submit the answer simultaneously... however, I bring out a way to customize the colors by PlotStyle. 囧rz $\endgroup$
    – PureLine
    Commented Jan 22, 2018 at 8:26
  • $\begingroup$ PureLine, thanks. Good point. $\endgroup$
    – kglr
    Commented Jan 22, 2018 at 8:37

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