ex23ch3.m

these codes are for solving OED with matlab

function sol = ex23ch3
% f = y(1), f' = y(2), f'' = y(3)
beta = 0.5;
infinity = 6;
solinit = bvpinit(linspace(0,infinity,5),@guess);
sol = bvp4c(@odes,@bcs,solinit,[],beta);
plot(sol.x,sol.y(2,:))
axis([0 infinity 0 1.1])
title('First derivative of the solution.')
fprintf('Reference value: f''''(0) = 0.92768\n')
fprintf('Computed value:  f''''(0) = %7.5f\n',sol.y(3,1))
%======================================================
function v = guess(x)
v = [x; 1; 0];

function dydx = odes(x,y,beta)
dydx = [ y(2); y(3); (-y(1)*y(3) - beta*(1 - y(2)^2)) ];

function res = bcs(ya,yb,beta)
res = [ ya(1); ya(2); yb(2)-1 ];