Use finite difference method to solve for eigenvalue E from the following second order ODE: - y'' + (x2/4) y = E y I discretize the equation so that it becomes yi-1 - [2 + h2(x2i/4)] yi + yi+1 = - E h2 yi where xi = i*h, and h is the distance between any two adjacent mesh points. This is my Matlab code: Code (Text): clear all n = 27; h = 1/(n+1); voffdiag = ones(n-1,1); for i = 1:n xi(i) = i*h; end mymat = -2*eye(n)-diag(((xi.^2).*(h^2)./4),0)+diag(voffdiag,1)+diag(voffdiag,-1); D=sort(eig(mymat),'descend'); lam= -D/(h^2); spy(mymat) fprintf(1,' The smallest eigenvalue is %g \n',lam(1)); fprintf(1,' The second smallest eigenvalue is %g \n',lam(2)); fprintf(1,' The 3rd eigenvalue is %g \n',lam(3)); it returns Code (Text): The smallest eigenvalue is 9.92985 The second smallest eigenvalue is 39.3932 The 3rd eigenvalue is 88.0729 Obviously, something wrong here, since the analytic solution should be E = N + 1/2 (for N = 0, 1, 2, 3...) The smallest eigenvalue should be 0.5, instead of 9.92985. I don't know whether my numerical solution agrees with the analytic solution or not, if I impose a boundary condition (ie. when x goes to infinity, y(x) should vanish to 0). And I don't know how to impose boundary condition. Please help, thank you very much! By the way, is there any another numerical way to find the eigenvalue E please?