example_ode45_octave

% function for the derivative, this example has three equations in 
%  three unknowns as x = [x(1), x(2), x(3)] for the dependent variables
f = @(t,x) [-x(1)+3*x(3);-x(2)+2*x(3);x(1)^2-2*x(3)];

% calling ode45 to find a solution to the diff. eq'n 
%     over independent t variable from 0 to 1.5
tstart = 0;
tend = 1.5;
%     with initial condition [0 1/2 3]
%  xa is the 'x approximate' at the values of t, 
%  xa has the 3-components of the x vector as columns, each row for a time
[t,xa] = ode45(f,[tstart tend],[0 1/2 3]);

% displaying output as a plot
figure(1) 
plot(t,xa(:,2))
title('y(t)')
xlabel('t'), ylabel('y')

% displaying output as a plot
figure(2)
plot(t,xa(:,1))
title('x(t)')
xlabel('t'), ylabel('x')

% output a header
txt = sprintf('Displaying data\n     Time       X          Y         Z')

% displaying output as a table
data = [t,xa(:,1), xa(:,2), xa(:,3)]
% Note: xa has 3-components of the x vector as columns, each row for a time

% this data does not have fixed time-step spacing
% use interpolation to get 'nicer' output data table
h=0.25; % the fixed step by h for desired output:
t0 = (tstart:h:tend)'; % t0 is array of times at step-h spacing
xa0 = interp1(t,xa,t0); %xa0 now has data at spacing from t0

%output nicer table
% output a header
txt = sprintf('Fixed spaced data\n     Time       X          Y         Z')

% displaying output as a table
data = [t0,xa0(:,1), xa0(:,2), xa0(:,3)]