How to plot a function with Plot3D

Questions
1

I am unable to plot a function of two variables f(x,y).
Kindly, some one help me plot this function.
Mathematica file is attached here.

u[x_] := Exp[-4 (x - 1)^2]

?[x_] := Exp[-Integrate[u[y]/0.2, {y, 0, x}]]

f[x_, t_] := Integrate[(x - z)/t ?[z] Exp[-(x - z)^2/(0.4 t)], {z, -?, ?}]/
             Integrate[?[z] Exp[-(x - z)^2/(0.4 t)], {z, -?, ?}]

Plot3D[f[x, t], {x, 1, 3}, {t, 1, 3}]
2

Hi,

this here appears to work:

u[x_] := Exp[-4 (x - 1)^2];
\[Phi][x_] := Evaluate@Exp[-Integrate[u[y]/0.2, {y, 0, x}]];
f[x_, t_] := 
 NIntegrate[(x - z)/
   t \[Phi][z] Exp[-(x - z)^2/(
    0.4 t)], {z, -\[Infinity], \[Infinity]}]/
 NIntegrate[\[Phi][z] Exp[-(x - z)^2/(
    0.4 t)], {z, -\[Infinity], \[Infinity]}];

appears to work. Basically you have to use numerical integration instead of symbolic integration.

Plot3D[f[x, t], {x, 1, 3}, {t, 1, 3}]

ScreenShot2015-11-21at16.43.21.png
ScreenShot2015-11-21at16.43.21.png574×448 49.6 KB

Cheers,

Marco
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=ScreenShot2015-11-21at16.43.21.png&userId=48754

3

I tried doing you code step by step. The integral in the numerator of the definition of f is taking a long time. Have you tried NIntegrate instead of Integrate?

4

Thanks a lot !

NIntegrate works.