Heat Equation

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