Two-stage complex Rosenbrock schemes for stiff systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 270-287
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New two-stage Rosenbrock schemes with complex coefficients are proposed for stiff systems of differential equations. The schemes are fourth-order accurate and satisfy enhanced stability requirements. A one-parameter family of $L1$-stable schemes with coefficients explicitly calculated by formulas involving only fractions and radicals is constructed. A single $L2$-stable scheme is found in this family. The coefficients of the fourth-order accurate $L4$-stable scheme previously obtained by P. D. Shirkov are refined. Several fourth-order schemes are constructed that are high-order accurate for linear problems and possess the limiting order of $L$-decay. The schemes proposed are proved to converge. A symbolic computation algorithm is developed that constructs order conditions for multistage Rosenbrock schemes with complex coefficients. This algorithm is used to design the schemes proposed and to obtain fifth-order accurate conditions.
@article{ZVMMF_2009_49_2_a5,
author = {A. B. Alshin and E. A. Alshina and A. G. Limonov},
title = {Two-stage complex {Rosenbrock} schemes for stiff systems},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {270--287},
publisher = {mathdoc},
volume = {49},
number = {2},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a5/}
}
TY - JOUR AU - A. B. Alshin AU - E. A. Alshina AU - A. G. Limonov TI - Two-stage complex Rosenbrock schemes for stiff systems JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2009 SP - 270 EP - 287 VL - 49 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a5/ LA - ru ID - ZVMMF_2009_49_2_a5 ER -
%0 Journal Article %A A. B. Alshin %A E. A. Alshina %A A. G. Limonov %T Two-stage complex Rosenbrock schemes for stiff systems %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2009 %P 270-287 %V 49 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a5/ %G ru %F ZVMMF_2009_49_2_a5
A. B. Alshin; E. A. Alshina; A. G. Limonov. Two-stage complex Rosenbrock schemes for stiff systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 2, pp. 270-287. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_2_a5/