ex01ch3.m

these codes are for solving OED with matlab

function ex01ch3
% Solve ((1 - x^7)y')' + lambda*x^7*y = 0. Let v = (1 - x^7)*y so
% that the equations are y' = v/(1 - x^7), v' = - lambda*x^7*y,
% with boundary conditions y(0) = 0, y(1) = 1.
lambda = input('Guess for eigenvalue: ');
sol = bvpinit(linspace(0,1,10),@guess,lambda);
sol = bvp4c(@odes,@bcs,sol);
fprintf('Computed the eigenvalue %g.\n',sol.parameters)
plot(sol.x,sol.y(1,:));
%===========================================================
function v = guess(x)
g = 5*pi/2;
y = x*sin(g*x);
yp = sin(g*x) + g*x*cos(g*x);
v = [ y; (1 - x^7)*yp];

function dydx = odes(x,y,lambda)
if x == 1
    yp = lambda/7;
else
    yp = y(2)/(1 - x^7);
end
dydx = [ yp; -lambda*x^7*y(1) ];

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