Homework 5: Diffusion Equation

Due March 16.

1. Write a program to solve the diffusion problem:
   
   $${\partial^2 u \over \partial x^2} = {\partial u \over \partial t}$$
   
   
   for $u(x,t)$ with the boundary conditions
   
   $$u(0, t) = 200, \quad u(1,t) = 200, \quad u(x,0) = 0.$$
   
   
   using the explicit forward differencing method with $\Delta x = 0.2$.

2. Plot the results for $u(0.4, t)$ for $0 < t < 0.3$ for two different timesteps: $\Delta t = .04$ and .015. How do these two timesteps compare with the stability criterion for the forward difference method?

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