% shoot Script solves a linear 2-point boundary value
%       problem by the simple shooting method.
%       Requires besselde.m

% Boundary conditions
a  = 1;  b = 6;
ya = 1; yb = 0;

% Fundamental solution
tspan = [a b];
options = odeset('RelTol',1e-6);
Y10 = [1;0];
[t1,Y1] = ode45('besselde',tspan,Y10,options);
Y20 = [0;1];
[t2,Y2] = ode45('besselde',tspan,Y20,options);

% Get solutions at x=6, calculate C2, then y.
n1 = length(t1); Y1fin = Y1(n1,1);
n2 = length(t2); Y2fin = Y2(n2,1);

C2 = -Y1fin/Y2fin;
disp(sprintf('C2 = %12.6e',C2))

y0 = [1;C2];
[t,y] = ode45('besselde',tspan,y0,options);
plot(t,y(:,1))
xlabel('x'), ylabel('y')
title('Solution of Bessel DE of order 1/2, y(1)=1, y(6)=0.')