function [t,y] = holmes

% M.H. Holmes, Introduction to Perturbation Methods,
% Springer, New York, 1995, solves the ODE
%
%   y'' + epsilon*lambda*y' + y + ...
%         epsilon*kappa*y^3 = epsilon*cos((1+epsilon*omega)t)
% 
% with parameter values that results in a highly oscillatory
% solution with slowly increasing magnitude.  Here the solution
% is compared to the RMS average computed with ODEAVG.

clc

tempavg = load('holmes.dat','-ascii');
tempode = load('holmesode.dat','-ascii');
tempd = load('holmesd.dat','-ascii');
delta = tempd(1);
navg = tempd(2);

tode = tempode(:,1);
yode = tempode(:,2);
tavg = tempavg(:,1);

% Compute the RMS average.
R = sqrt(tempavg(:,2));
plot(tavg,R,'r',tode,yode,'k')
%legend('Averaged RMS solution','Computed solution',...
%       'Location','SouthWest')
%title(['Using \Delta = ',num2str(delta),' and average = ',...
%        int2str(navg),'.'])
xlabel('t')