Geodesic
Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1392-1414

Voir la notice de l'article provenant de la source Math-Net.Ru

Many applied problems are described by differential algebraic systems. Complex Rosenbrock schemes are proposed for the numerical integration of differential algebraic systems by the $\varepsilon$-embedding method. The method is proved to converge quadratically. The scheme is shown to be applicable even to superstiff systems. The method makes it possible to perform computations with a guaranteed accuracy. An equation is derived that describes the leading term of the error in the method as a function of time. An algorithm extending the method to systems of differential equations for complex-valued functions is proposed. Examples of numerical computations are given. 
@article{ZVMMF_2006_46_8_a4,
     author = {A. B. Alshin and E. A. Alshina and N. N. Kalitkin and A. B. Koryagina},
     title = {Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1392--1414},
     publisher = {mathdoc},
     volume = {46},
     number = {8},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a4/}
}
TY  - JOUR
AU  - A. B. Alshin
AU  - E. A. Alshina
AU  - N. N. Kalitkin
AU  - A. B. Koryagina
TI  - Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 1392
EP  - 1414
VL  - 46
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a4/
LA  - ru
ID  - ZVMMF_2006_46_8_a4
ER  - 
%0 Journal Article
%A A. B. Alshin
%A E. A. Alshina
%A N. N. Kalitkin
%A A. B. Koryagina
%T Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 1392-1414
%V 46
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a4/
%G ru
%F ZVMMF_2006_46_8_a4
A. B. Alshin; E. A. Alshina; N. N. Kalitkin; A. B. Koryagina. Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 8, pp. 1392-1414. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_8_a4/