Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 3, pp. 620-628
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A. I. Zadorin; V. N. Ignat'ev. Numerical solution of an equation with a small parameter multiplying the highest derivative. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 3, pp. 620-628. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_3_a10/
@article{ZVMMF_1983_23_3_a10,
author = {A. I. Zadorin and V. N. Ignat'ev},
title = {Numerical solution of an equation with a small parameter multiplying the highest derivative},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {620--628},
year = {1983},
volume = {23},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_3_a10/}
}
TY - JOUR
AU - A. I. Zadorin
AU - V. N. Ignat'ev
TI - Numerical solution of an equation with a small parameter multiplying the highest derivative
JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY - 1983
SP - 620
EP - 628
VL - 23
IS - 3
UR - http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_3_a10/
LA - ru
ID - ZVMMF_1983_23_3_a10
ER -
%0 Journal Article
%A A. I. Zadorin
%A V. N. Ignat'ev
%T Numerical solution of an equation with a small parameter multiplying the highest derivative
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1983
%P 620-628
%V 23
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_3_a10/
%G ru
%F ZVMMF_1983_23_3_a10
A family of monotonic difference schemes on a non-uniform mesh is proposed for solving a second-order ordinary differential equation with a small parameter in the highest derivative. It is shown that, under certain conditions on the coefficients of the equation, the difference scheme is ill-posed. Two methods are given for solving an ill-posed difference problem, which are stable to rounding errors.
