%
% SHOOTM2.M Example of Shooting Method for Solving ODEs
%
% This is a follow up to demo SHOOTM1.M. This file simply generates the
% plots obtained for each of the guesses for the ALF used in SHOOTM1.M
% The goal was to find the ALF at x = 0 which gives y(pi) = 0.
%
% also see SHOOTF.M - contains description of given differential equation
% y'' + 3xy' + 7y = cos(2x) with y(0) = 1 and y(pi) = 0
%
% File prepared by J. R. White, UMass-Lowell (Aug. 2003)
%
%
% getting started
clear all, close all, nfig = 0;
%
% with manual procedure, ALFs of 1, -1, and -5.4713 were used in SHOOTM1.M
% let's plot the function for these different guesses to see how this works
gs = [1 -1 -5.4715];
%
% set domain limits and solve IVP
xo = 0; xf = pi; tol = 1.0e-6; yxo = 1.0;
options = odeset('RelTol',tol);
[x1,z1] = ode23('shootf',[xo xf],[yxo gs(1)],options);
[x2,z2] = ode23('shootf',[xo xf],[yxo gs(2)],options);
[x3,z3] = ode23('shootf',[xo xf],[yxo gs(3)],options);
%
% now plot results
nfig = nfig+1; figure(nfig)
plot(x1,z1(:,1),'g-',x2,z2(:,1),'r-.',x3,z3(:,1),'b--','LineWidth',2)
title('ShootM2: Shooting Method for ODEs (Case 1 - Manual Iteration)')
xlabel('x values'),ylabel('y values'),grid
legend('alf = 1','alf = -1','alf = -5.4715')
%
% end of demo