Heat Equation
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HeatEquation-1.nb
1
ut = uxx i y j z j z j z u H0, tL = 0 j z j z j z j z j z u H1, tL = 0 j z j z j z k u Hx, 0L = Sin Hπ xL { In[52]:=
α = 1;
In[53]:=
sol = NDSolve@8uH0,1L @x, tD
uH2,0L @x, tD, u@x, 0D
Sin@π xD, u@0, tD
Out[53]=
88u → InterpolatingFunction@880., 1.<, 80., 0.2<<, <>D<<
In[57]:=
pl = Plot3D@Evaluate@u@x, tD ê. sol@@1DDD, 8t, 0, .2<, 8x, 0, 1
0, u@1, tD
0<, u, 8x, 0, 1<, 8t, 0, .2
HeatEquation-1.nb
2
1
0.75
1
0.5 0.75
0.25
0 0
0.5
0.05
0.25
0.1
0.15
0.2 Out[57]=
SurfaceGraphics
0
HeatEquation-1.nb
In[60]:=
Show@pl, AxesLabel → 8"x", "t", "z"<, PlotLabel −> "Heat Surface", ViewPoint −> 82.221, 0.844, 2.409<, Shading → False, Boxed → FalseD
3
HeatEquation-1.nb
4
Heat Surface 0
0.05
x 0.1
0.15
0.2 1
0.75 z 0.5 5 0.25 25 0 0
0.25
0.5
t
0.75
1
HeatEquation-1.nb
Out[60]=
SurfaceGraphics
5
1
ut = uxx i y j z j z j z u H0, tL = 0 j z j z j z j z j z u H1, tL = 0 j z j z j z k u Hx, 0L = Sin Hπ xL { In[52]:=
α = 1;
In[53]:=
sol = NDSolve@8uH0,1L @x, tD
uH2,0L @x, tD, u@x, 0D
Sin@π xD, u@0, tD
Out[53]=
88u → InterpolatingFunction@880., 1.<, 80., 0.2<<, <>D<<
In[57]:=
pl = Plot3D@Evaluate@u@x, tD ê. sol@@1DDD, 8t, 0, .2<, 8x, 0, 1
0, u@1, tD
0<, u, 8x, 0, 1<, 8t, 0, .2
HeatEquation-1.nb
2
1
0.75
1
0.5 0.75
0.25
0 0
0.5
0.05
0.25
0.1
0.15
0.2 Out[57]=
SurfaceGraphics
0
HeatEquation-1.nb
In[60]:=
Show@pl, AxesLabel → 8"x", "t", "z"<, PlotLabel −> "Heat Surface", ViewPoint −> 82.221, 0.844, 2.409<, Shading → False, Boxed → FalseD
3
HeatEquation-1.nb
4
Heat Surface 0
0.05
x 0.1
0.15
0.2 1
0.75 z 0.5 5 0.25 25 0 0
0.25
0.5
t
0.75
1
HeatEquation-1.nb
Out[60]=
SurfaceGraphics
5
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