Reference no: EM13279287

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.

1) Solve ut + uux = 0, t > 0 where u(x, 0)

1,    0,  2,   0,

x < -1 - 1 < x < 0 0 < x < 1 x > 1