Heat Equation With Mathematica
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HeatEquation-1.nb
1
ut = uxx y i z j z j z j u H0, tL = 0 z j z j z j z j z j u H1, tL = 0 z j z j z j u Hx, 0L = Sin Hπ xL { k In[52]:=
α = 1;
In[53]:=
sol = NDSolve@8uH0,1L @x, tD u, 8x, 0, 1<, 8t, 0, .2
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<,
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
2
Show@pl, AxesLabel → 8"x", "t", "z"<, PlotLabel −> "Heat Surface", Mesh → FalseD
In[56]:=
Heat Surface
1 0.75
1
z 0.5 0.75
0.25 0 0
0.5 t 0.05
0.25
0.1 x 0.15
0.2 Out[56]=
SurfaceGraphics
0
HeatEquation-1.nb
In[58]:=
3
Show@pl, ViewPoint −> 82.221, 0.844, 2.409
0.05
0.1
0.15
0.2 1 0.75 0.5 5 0.25 25 0 0 0.25 0.5 0.75 1 Out[58]=
SurfaceGraphics
HeatEquation-1.nb
4
Show@pl, AxesLabel → 8"x", "t", "z"<, PlotLabel −> "Heat Surface", ViewPoint −> 82.221, 0.844, 2.409<, Shading → FalseD
In[59]:=
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
Out[59]=
SurfaceGraphics
1
ut = uxx y i z j z j z j u H0, tL = 0 z j z j z j z j z j u H1, tL = 0 z j z j z j u Hx, 0L = Sin Hπ xL { k In[52]:=
α = 1;
In[53]:=
sol = NDSolve@8uH0,1L @x, tD u, 8x, 0, 1<, 8t, 0, .2
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<,
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
2
Show@pl, AxesLabel → 8"x", "t", "z"<, PlotLabel −> "Heat Surface", Mesh → FalseD
In[56]:=
Heat Surface
1 0.75
1
z 0.5 0.75
0.25 0 0
0.5 t 0.05
0.25
0.1 x 0.15
0.2 Out[56]=
SurfaceGraphics
0
HeatEquation-1.nb
In[58]:=
3
Show@pl, ViewPoint −> 82.221, 0.844, 2.409
0.05
0.1
0.15
0.2 1 0.75 0.5 5 0.25 25 0 0 0.25 0.5 0.75 1 Out[58]=
SurfaceGraphics
HeatEquation-1.nb
4
Show@pl, AxesLabel → 8"x", "t", "z"<, PlotLabel −> "Heat Surface", ViewPoint −> 82.221, 0.844, 2.409<, Shading → FalseD
In[59]:=
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
Out[59]=
SurfaceGraphics
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