Geodesic
An error bound of the Ritz method for a singular second-order differential equation
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 208-215 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {M. N. Yakovlev},
     title = {An error bound of the {Ritz} method for a~singular second-order differential equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a13/}
}
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M. N. Yakovlev. An error bound of the Ritz method for a singular second-order differential equation. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 208-215. http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a13/

[1] N. M. Krylov, Izbrannye trudy, t. 2, Kiev, 1980

[2] L. V. Kantorovich, V. I. Krylov, Priblizhennye metody vysshego analiza, M., 1962 | MR | Zbl

[3] M. N. Yakovlev, “Razreshimost singulyarnykh kraevykh zadach dlya obyknovennykh differentsialnykh uravnenii poryadka $2m$”, Zap. nauchn. semin. POMI, 309, POMI, SPb., 2004, 174–188 | MR | Zbl

[4] M. N. Yakovlev, “Pervaya kraevaya zadacha dlya nelineinogo singulyarnogo obyknovennogo differentsialnogo uravneniya chetvertogo poryadka”, Zap. nauchn. semin. POMI, 334, POMI, SPb., 2006, 233–245 | MR | Zbl

[5] M. N. Yakovlev, “Metod konechnykh elementov dlya singulyarnykh kraevykh zadach”, Zap. nauchn. semin. POMI, 346, POMI, SPb., 2007, 149–159