% COMPARE.m
% Sample script for comparing a nonlinear oscillator and
% the linearized approximation. 
% Note, the system parameters(damping spring constants etc. 
% are defined in the m-file damped2.m).
%
% This file may be used for a quick demo.   But is was
% originally intended to provide help with the syntax:
% After the first execution of this script, users may
% want to copy (to the command window), and edit 
% specific commands from this file. Alternatively,
% delete all unneeded commands, customize the script, 
% and save the file under a new name.
%
% All rights reserved. Matthias Kawski. April 1999.


% Set the search path to include the working directory
% where the user has write-permission, and where this
% file and the file damped2.m reside on a local drive.
%
addpath('C:\temp')
edit compare
%
% Edit the m-file that contains a description of the 
% differential equations. This is the place to modify
% the system parameters, e.g. the damping constants.
%
edit damped2.m
%
% Define the initial conditions -- the same for both systems.
% y0 is the initial position. y1 is the initial velocity.
%
y0=0
y1=1
%
% Define a suitable time interval.
%
t0=0
tfin=20
%
% Call the numerical DE-solver and write the results in
% column format to the variables T and Y. To be safe first
% clear the variables.
%
clear T
clear Y
[T,Y]=ode45('damped2',[t0,tfin],[y0,y1,y0,y1]);
%
% Take a look at the size of the data generated. T contains
% a single column, Y contains 4 columns of the same length
%
size(T)
size(Y)
%
% Plot the computed positions of the nonlinear (red) and of 
% the linear model (blue). Overlay also the velocities of the
% nonlinear (magenta) and linear (green) models.
% First clear the graphing window
%
clf
plot(T,Y(:,1),'r-',T,Y(:,3),'b-',T,Y(:,2),'m:',T,Y(:,4),'g:')