Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 119-142
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A. V. Kim; V. G. Pimenov. Application of $i$-smooth analysis to construction of numerical methods for solving functional-differential equations. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 119-142. http://geodesic.mathdoc.fr/item/TIMM_1998_5_a10/
@article{TIMM_1998_5_a10,
author = {A. V. Kim and V. G. Pimenov},
title = {Application of $i$-smooth analysis to construction of numerical methods for solving functional-differential equations},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {119--142},
year = {1998},
volume = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_1998_5_a10/}
}
TY - JOUR
AU - A. V. Kim
AU - V. G. Pimenov
TI - Application of $i$-smooth analysis to construction of numerical methods for solving functional-differential equations
JO - Trudy Instituta matematiki i mehaniki
PY - 1998
SP - 119
EP - 142
VL - 5
UR - http://geodesic.mathdoc.fr/item/TIMM_1998_5_a10/
LA - ru
ID - TIMM_1998_5_a10
ER -
%0 Journal Article
%A A. V. Kim
%A V. G. Pimenov
%T Application of $i$-smooth analysis to construction of numerical methods for solving functional-differential equations
%J Trudy Instituta matematiki i mehaniki
%D 1998
%P 119-142
%V 5
%U http://geodesic.mathdoc.fr/item/TIMM_1998_5_a10/
%G ru
%F TIMM_1998_5_a10
New approach to constructing methods of Runge–Kutta type as well as multistep methods for solving functional-differential equations is proposed. Our methods (direct analogs of numerical methods for solving ordinary differential equations) are based on separation of finite-dimensional and infinite-dimensional (functional) components in the structure of the phase state. Determination of the approximation order of the methods essentially uses notions of $i$-smooth analysis.
