High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 4, pp. 493-508
Voir la notice du chapitre de livre provenant de la source Math-Net.Ru
The paper deals with the construction of high-order accuracy finite element schemes for the fourth-order ordinary differential equation with degenerate coefficients on the boundary. The method for solving the problem is based on both multiplicative and additive-multiplicative separation of singularities. For the given class of smoothness of the right-hand sides, the optimal convergence rate has been proved.
Keywords:
two-point boundary value problem, finite element schemes, weight function space, multiplicative and additive-multiplicative decomposition of singularity.
@article{UZKU_2017_159_4_a5,
author = {A. A. Sobolev and M. R. Timerbaev},
title = {High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {493--508},
publisher = {mathdoc},
volume = {159},
number = {4},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a5/}
}
TY - JOUR AU - A. A. Sobolev AU - M. R. Timerbaev TI - High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2017 SP - 493 EP - 508 VL - 159 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a5/ LA - ru ID - UZKU_2017_159_4_a5 ER -
%0 Journal Article %A A. A. Sobolev %A M. R. Timerbaev %T High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2017 %P 493-508 %V 159 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a5/ %G ru %F UZKU_2017_159_4_a5
A. A. Sobolev; M. R. Timerbaev. High-order accuracy approximation for the two-point boundary value problem of the fourth order with degenerate coefficients. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 4, pp. 493-508. http://geodesic.mathdoc.fr/item/UZKU_2017_159_4_a5/