LABS 6_7

1. 
%Find the temperature distribution after five time steps on a unit bar
%with the initial temperature equal to 10. Suppose that left and right end of 
%the bar have fix temperature of 100 and 50, respectively. 
%Use spatial mesh with delta_x = 0.1.
%Find maximal time step that assures stability of the numerical scheme.
%Use fully discrete method on the heat equation with c=1 with the explicit 
%Euler's scheme. Plot all step solutions. Test larger time steps, still stable?
%Which solution is expected after the infinite number of time steps?

2. 
%Find the solution of a 2-D Laplace Equation, on unit square, with
%boundary conditions equal to 1 on left and right boundaries and 0 on 
%upper and lower boundaries. Use h=0.2 in both dimensions.
%Analyse the system matrix. Can you apply Cholesky factorization for its solution? 
%If yes, why? How many fills are generated in Cholesky factorization matrix?

3.
%Apply minimum degree heuristics, by permuting of rows and columns of the
%system matrix from exercise 2. Obtain the number of fills on permuted matrix and check the 
%solution, again using Cholesky.

4. 
%Implement 20 steps of Jacobi iteration for the system matrix and boundary 
%conditions from exercise 2. Estimate the maximal error in the iterative solution.
%Plot the approximate solution.


Pack your solutions in a zip file, set permissions for reading, and save your file
in the directory:
/home/scicomp/trobec/labs due to Friday, June 24, 2005.