A class of one-step one-stage methods for stiff systems of ordinary differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1251-1265
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A new class of one-step one-stage methods ($ABC$-schemes) designed for the numerical solution of stiff initial value problems for ordinary differential equations is proposed and studied. The Jacobian matrix of the underlying differential equation is used in $ABC$-schemes. They do not require iteration: a system of linear algebraic equations is once solved at each integration step. $ABC$-schemes are $A$- and $L$-stable methods of the second order, but there are $ABC$-schemes that have the fourth order for linear differential equations. Some aspects of the implementation of $ABC$-schemes are discussed. Numerical results are presented, and the schemes are compared with other numerical methods.
@article{ZVMMF_2011_51_7_a6,
author = {M. V. Bulatov and A. V. Tygliyan and S. S. Filippov},
title = {A~class of one-step one-stage methods for stiff systems of ordinary differential equations},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1251--1265},
publisher = {mathdoc},
volume = {51},
number = {7},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a6/}
}
TY - JOUR AU - M. V. Bulatov AU - A. V. Tygliyan AU - S. S. Filippov TI - A class of one-step one-stage methods for stiff systems of ordinary differential equations JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2011 SP - 1251 EP - 1265 VL - 51 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a6/ LA - ru ID - ZVMMF_2011_51_7_a6 ER -
%0 Journal Article %A M. V. Bulatov %A A. V. Tygliyan %A S. S. Filippov %T A class of one-step one-stage methods for stiff systems of ordinary differential equations %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2011 %P 1251-1265 %V 51 %N 7 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a6/ %G ru %F ZVMMF_2011_51_7_a6
M. V. Bulatov; A. V. Tygliyan; S. S. Filippov. A class of one-step one-stage methods for stiff systems of ordinary differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 7, pp. 1251-1265. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_7_a6/