MATLAB programs for
Numerical Simulation of ODEs
* Now with euler2d and its graphing program (updated 04/19/06)

Directions:  1.  Copy files to a directory/folder
                       (If your browser does not allow you to directly copy the files,
                               you should copy the file contents into the
clipboard, start
                               MATLAB, choose new from the file menu, paste the contents
                               of the clipboard, and save
as filename.m  (for the euler code,
                               you must use euler.m as a file name... it's a function)

                    2.  Start running MATLAB (double-click)
                    3.  Set the directory/folder from default (work)
                         to the folder you have above.
                    4.  From the command line, type in the file
                         name that graphs the comparison code.
                    5.  The result should be a graph of the actual solution and
                          a numerical approximation.

Section 6.1:  Basic Euler 
    
euler code (this is the actual code that performs the calculations)
        comparison code (this is the code that plots the approximate and actual solutions)

          two dimensional euler code (This is the code constructed in class.) (updated 04/19/06)

          graphs two dimensional euler simulation  (This is the graphing portion of the code from class.)  (updated 04/19/06)

Section 6.2:  Improved Euler (RK2)
           improved (implicit) euler code(this is the actual code that performs the calculations)

         comparison code for both euler methods (this is the code that plots the approximate and actual solutions)

Section 6.2:  Runge-Kutta (RK4)
           Runge-Kutta code (this is the actual code that performs the calculations)

      comparison code for all three methods (this is the code that plots the approximate and actual solutions)