1. Use separation of variables to solve the following heat equation problem with inhomogeneous boundary conditions:
∂u/∂t = 3∂2u/∂x2
u(0, t) = 20
u(40, t) = 100 u(x,0)= 40- x
After you have found the infinite series solution using separation of variables, then use Matlab to evaluate your series solution in order to plot the temperature profile at a few fixed values of time. In other words, plot u(x,t) versus x for a few fixed values of t. Put all the temperature curves on a single plot and label the t value for each curve.
2. In addition to the problems assigned in class, please solve the following.
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1) Solve ut + uux = 0, t > 0 where u(x, 0)
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1,
0,
2,
0,
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x < -1
- 1 < x < 0
0 < x < 1
x > 1
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