% Matlab diary from cs110a, Mar 2 2005.
%
% This is what I typed in class.  
%
% Type it into Matlab yourself to
% reproduce the output I showed.

edit f  % this is the falling-object f from last time
ode45(@f, [0 2], [1 ; 0]);
opts = odeset('events', @stopper);
opts

edit stopper

type stopper


function [gstop, isterminal, direction] = stopper(t,y)
% STOPPER : stopping criterion function for falling body
%
% gstop = 0 is the event this handler recognizes
% return gstop = height above ground, so ode will stop when it hits ground
gstop = y(1);  %  the "event" happens when gstop = 0
isterminal = 1; % the "event" ends the execution of ode45
direction = [] ; % don't care which direction gstop hits zero from


[T, Y, tfinal] = ode45(@f, [0 2], [1 ; 0], opts);
clf
tfinal
tfinal =
    1.6575
size(Y)
plot(T,Y(:,1))


edit stopper

type stopper

function [gstop, isterminal, direction] = stopper(t,y)
% STOPPER : stopping criterion function for falling body
%
% gstop = 0 is the event this handler recognizes
% return gstop = height above ground, so ode will stop when it hits ground
gstop = y(1)-.5;  %  the "event" happens when gstop = 0
isterminal = 1; % the "event" ends the execution of ode45
direction = [] ; % don't care which direction gstop hits zero from


[T, Y, tfinal] = ode45(@f, [0 2], [1 ; 0], opts);
tfinal
plot(T,Y(:,1))

ode45(@f, [0 2], [1 ; 0]);

edit f
type f

function ydot = f(t,y)
% F  :  function ydot = f(t,y) for ODE solution
%
%   t:  scalar time
%   y:  vector, y = y(t), unknown function
%   
%   ydot:  vector of dy / dt
ydot = y / 2;


ode45(@f, [0 10], 1);
hold on

type ode1

function ode1(F, tspan, y0, h)
% ODE1 : demo version of simple Euler method
% ode1(F, tspan, y0, h) uses step size h and plots 1D results

t0 = tspan(1);
tfinal = tspan(2);

t = t0;
y = y0;
plot(t,y,'r.');
hold on
while t <= tfinal
    y = y + h*feval(F,t,y);
    t = t + h;
    plot(t,y,'r.')
end;


h = 1
ode1 ( @f, [0 10], 1, h);
h = .5
ode1 ( @f, [0 10], 1, h);
h = .1
ode1 ( @f, [0 10], 1, h);
h = .001;
ode1 ( @f, [0 10], 1, h);