PROJECT 1                   Sept. 30




   1. Using your program or an adaptation of one that I will supply
      *  solve the linear equations which describe the approximate
         temperature distribution on a square metal plate at 100 interior
         points. There will therefore be 100 equations and 100 unknowns.
         These equations will be given to you in these notes and discussed
         in class. 

      *  You will need to create a file which contains the coefficient
         matrix and the last line of the file should contain the values
         of the right hand side of the equations.

      *  To debug the process, you should first work the same problem for
         a 4 by 4 grid of mesh points. In this case there will be 16 unknowns.
         I will send the coefficient matrix to you.

      *  Presentation of the solution--You should plot the resulting 
         temperatures in two different ways using MATLAB. You should
         plot both a contour plot and a surface plot (including boundary
         temperatures). The contour plot should have some of the contours
         with numeric labels. Turn in hard copy print-outs of these plots.


      *  You should also solve the same set of 100 equations by an iterative
         method. You should use ONE of the three following iterative methods:
         (a) Gauss-Seidel (b) SOR  (c) Multi-grid . Options b) and c) will
         receive more credit that option a) . Option c) will be worth 
         substantial extra credit. Handouts will be given to you covering
         these iterative methods.  
         The iterative method should terminate when iterates are correct to
         three decimal places.

      *  All work done on MATLAB (except plotting) should be accompanied by
         the number of megaflops needed. (See Nakamura)
      
         This project is due on Oct. 14. Be sure that your results are 
         presented in a clear, organized and easy to read fashion. Do
         not hesitate to ask me questions concerning this project if you
         are unclear about something.