Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXI, Tome 359 (2008), pp. 208-215
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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/
@article{ZNSL_2008_359_a13,
author = {M. N. Yakovlev},
title = {An error bound of the {Ritz} method for a~singular second-order differential equation},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {208--215},
year = {2008},
volume = {359},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a13/}
}
TY - JOUR
AU - M. N. Yakovlev
TI - An error bound of the Ritz method for a singular second-order differential equation
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2008
SP - 208
EP - 215
VL - 359
UR - http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a13/
LA - ru
ID - ZNSL_2008_359_a13
ER -
%0 Journal Article
%A M. N. Yakovlev
%T An error bound of the Ritz method for a singular second-order differential equation
%J Zapiski Nauchnykh Seminarov POMI
%D 2008
%P 208-215
%V 359
%U http://geodesic.mathdoc.fr/item/ZNSL_2008_359_a13/
%G ru
%F ZNSL_2008_359_a13
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.
