Approximation of the Jacobian matrix in $(m,2)$-methods for solving stiff problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 12, pp. 2194-2208
Voir la notice de l'article provenant de la source Math-Net.Ru
An initial value problem for stiff systems of first-order ordinary differential equations is considered. In the class of $(m,k)$-methods, two integration algorithms with a variable step size based on second $(m=k=2)$ and third $(k=2,m=3)$ order-accurate schemes are constructed in which both analytical and numerical Jacobian matrices can be frozen. A theorem on the maximum order of accuracy of $(m,2)$-methods with a certain approximation of the Jacobian matrix is proved. Numerical results are presented.
@article{ZVMMF_2011_51_12_a5,
author = {E. A. Novikov},
title = {Approximation of the {Jacobian} matrix in $(m,2)$-methods for solving stiff problems},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {2194--2208},
publisher = {mathdoc},
volume = {51},
number = {12},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_12_a5/}
}
TY - JOUR AU - E. A. Novikov TI - Approximation of the Jacobian matrix in $(m,2)$-methods for solving stiff problems JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2011 SP - 2194 EP - 2208 VL - 51 IS - 12 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_12_a5/ LA - ru ID - ZVMMF_2011_51_12_a5 ER -
%0 Journal Article %A E. A. Novikov %T Approximation of the Jacobian matrix in $(m,2)$-methods for solving stiff problems %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2011 %P 2194-2208 %V 51 %N 12 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_12_a5/ %G ru %F ZVMMF_2011_51_12_a5
E. A. Novikov. Approximation of the Jacobian matrix in $(m,2)$-methods for solving stiff problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 12, pp. 2194-2208. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_12_a5/