A bound for the error of the Ritz method in the case of the Lidstone problem for a singular differential equation of fourth order

For the Lidstone boundary-value problem

$$ \begin{array}{*{20}{c}} {{u^{(4)}} + q(t)u = f(t),\,\,\,0 < t < 1,} \\ {u(0) = u''(0) = u(1) = u''(1) = 0} \\ \end{array} $$

with nonintegrable functions q(t) and f(t), conditions of solvability are obtained and a computable error bound for the Ritz method is established. Bibliography: 3 titles.