% Sample session with MATLAB

% (1) GETTING STARTED:

% First log into a unity machine with your id and password.
% Start an xterm.
% Type "add matlab7" at the prompt to ensure that you
% will use MATLAB 7 hereafter. This has only to be done once.
% Type "matlab" at the prompt
% A MATLAB desktop should now appear.
% Download the programs "euler.m" and "myfunc.m"
% from the course webpage into your home directory.


% (2) A SAMPLE SESSION WITH EULER'S method in MATLAB

% I assume you now have the MATLAB desktop running
% You should type the following lines
% in your MATLAB desktop in the following order:
% I have interspaced my comments in the discussion .
% These comments appear on a line that starts with a % sign.
% You need not type these comment lines in your MATLAB desktop.

% Kartik's MATLAB session: 31st August 2005

% Let's try to solve the ODE
% dy/dx = y(2-y)
% y(0) = 3
% for all x in the interval [0 5]
% The file 'myfunc.m' contains the function y(2-y)
% The intial conditions are x0 = 0, y0 = 3
% x1, the end of my time interval, is 5
% We will first use 10 steps in Euler's method
% This is how you call the function euler.m in MATLAB
% The output variables xe1,ye1 contain the x and y values
% computed in Euler's method
[xe1,ye1] = euler(@myfunc,0,3,5,10);

% Let's plot xe1 vs ye1
plot(xe1,ye1);

% Now we will try 100 steps in Euler's method
% So n = 100
% The results are in variables xe2 and ye2

[xe2,ye2] = euler(@myfunc,0,3,5,100);

% Let's plot this on a separate figure

figure(2);
plot(xe2,ye2);

% Now let us try to use MATLAB's built in function ode45
% Type "help ode45" for more information

% We are interested in solving the ODE over
% the interval [0 5]
% Also y0 = 3

xspan = [0 5];
yzero = 3;
[xm,ym] = ode45(@myfunc,xspan,yzero);
figure(3);
plot(xm,ym);

% Print out the plots and exit MATLAB
exit