I need help with the following question:
For the eigenvalue problem $-u''=\lambda u$ in the interval $(0,1)$ with $u(0)=u(1)=0$, choose the pair of trail functions $x-x^2$ and $x^2-x^3$ and compute the Rayleigh-Ritz approximations to the first two eigenvalues. Compute with the exact values.
Now I have tried using the formulas provides to me where $det(A-\lambda B)=0$ , $Q=(\int_0^1 r u_r^2 dr)/(\int_0^1ru^2 dr)$. However I am getting completely wrong values when I try to make the matrices and do not understand what I have been doing wrong. Any help is appreciated. Thank you.
