Solve ODE for the eigenvalue

Hi, 

I'm trying to solve for the eigenvalue X; for specific values M and Mf, with boundary conditions at infinity, that is, y(-inf)=y(inf)=0, which is why ive used ya(1)-10^10 etc as the conditions, im not sure if this is approprate or not though.

Any help would be greatly appreciated. Ive attached the file.

[darova]

Please attach the original equation

[Alexander Kimbley]

The original equation is given by

y'' + [M * sqrt(1-(2*Mf^2)/X) *(X+1-(2*Mf^2)/X -2*Mf^2) -Y^2]y=0, where y=y(Y).

Answer 1

[darova]

I changed limits and the call of bvp4c

xlow = -2;
xhigh = 2;
X0 =8 ;
y10 = 1;
y20 = 1;
sol = bvp4c(@bvp4ode, @bvp4bc, solinit, options); %

Boundary function

function res = bvp4bc(ya,yb,p)
    res = [ya(1)            % y(a) = 0
            yb(1)           % y(b) = 0
            ya(2)-1];       % additional (not sure if it's correct)
end

The result

Look here and here

[Alexander Kimbley]

Hi, thanks for your help, ive had a look and it seems very close to the correct answer when Mf=0, but not quite, ive attached the new file, im not sure if ive entered everthing right; to check its right when Mf=0, the eigenvalue c should equal -1+ 1/M.

[darova]

For interval [-2 2]

>> mainbetarot
c =
   -0.2322
>> -1+1/1.4
ans =
   -0.2857

Try to change interval