An error bound of the Ritz method for a~singular second-order differential equation

M. N. Yakovlev

Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 208-215

Résumé

The paper presents an error bound of the Ritz method for the problem of minimizing the functional $$ J(u)=\int^1_0[u'(t)]^2\,dt+\int^1_0q(t)u^2(t)\,dt-2\int_0^1f(t)u(t)\,dt $$ in the space $\overset\circ{W^1_2}(0,1)$ in the case where the standard assumption on the continuity of $q(t)$ is replaced by the condition $q^2(t)t(1-t)\in L(0,1)$. In the case where $q(t)$ is continuous, the new bound is sharper than the known one. Bibl. – 5 titles.