ex04ch3.m

these codes are for solving OED with matlab

function sol = ex04ch3
global yatd
d = 0.001;
yatd = asymp(d);
solinit = bvpinit(linspace(d,1/2,10),@guess);
sol = bvp4c(@odes,@bcs,solinit);
xint = linspace(d,1/2);
yint = deval(sol,xint);
x = [0 xint];
y = [0 yint(1,:)];
asympy = [0 asymp(xint)];
plot(x,y,x,asympy)
axis([0 0.5 0 0.5])
legend('Computed','Asymptotic',4)
%========================================================
function v = guess(x)
v = [x*(1-x); 1-2*x];

function dydx = odes(x,y)
dydx = [y(2); -1/y(1)];

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

function v = asymp(x)
v = x.*sqrt(-2*log(x));