Numerical study of one-step lineary implicit methods which are L-equivalent to stiffly accurate two-stages Runge–Kutta schemes
Matematičeskoe modelirovanie, Tome 24 (2012) no. 12, pp. 129-136 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

One step free of iterations methods for numerical solution of Cauchy problem for ordinary differential systems of equations there are described. They are equivalent to stiffly accurate 2-stages Runge–Kutta schemes for linear problems (autonomous as well as non-autonomous). Stiff tests such as autonomous Kaps system and non-autonomous Prothero-Robinson problem have been used for numerical study of methods accuracy.
Keywords: one-step methods, stiffly accurate Runge–Kutta schemes, numerical order of accuracy, schemes with complex coefficients.
@article{MM_2012_24_12_a21,
     author = {A. M. Zubanov and P. D. Shirkov},
     title = {Numerical study of one-step lineary implicit methods which are {L-equivalent} to stiffly accurate two-stages {Runge{\textendash}Kutta} schemes},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {129--136},
     year = {2012},
     volume = {24},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2012_24_12_a21/}
}
TY  - JOUR
AU  - A. M. Zubanov
AU  - P. D. Shirkov
TI  - Numerical study of one-step lineary implicit methods which are L-equivalent to stiffly accurate two-stages Runge–Kutta schemes
JO  - Matematičeskoe modelirovanie
PY  - 2012
SP  - 129
EP  - 136
VL  - 24
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/MM_2012_24_12_a21/
LA  - ru
ID  - MM_2012_24_12_a21
ER  - 
%0 Journal Article
%A A. M. Zubanov
%A P. D. Shirkov
%T Numerical study of one-step lineary implicit methods which are L-equivalent to stiffly accurate two-stages Runge–Kutta schemes
%J Matematičeskoe modelirovanie
%D 2012
%P 129-136
%V 24
%N 12
%U http://geodesic.mathdoc.fr/item/MM_2012_24_12_a21/
%G ru
%F MM_2012_24_12_a21
A. M. Zubanov; P. D. Shirkov. Numerical study of one-step lineary implicit methods which are L-equivalent to stiffly accurate two-stages Runge–Kutta schemes. Matematičeskoe modelirovanie, Tome 24 (2012) no. 12, pp. 129-136. http://geodesic.mathdoc.fr/item/MM_2012_24_12_a21/

[1] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999, 685 pp.

[2] Dekker K., Verver Ya., Ustoichivost metodov Runge–Kutty dlya zhestkikh nelineinykh differentsialnykh uravnenii, Mir, M., 1988, 332 pp. | MR

[3] Rosenbrock H., “Some general implicit processes for numerical solution of differential equations”, Computer J., 5:4 (1962/1963), 329–330 | DOI | MR

[4] Kalitkin N. N., Panchenko S. L., “Optimalnye skhemy dlya zhestkikh neavtonomnykh sistem”, Matem. modelirovanie, 11:6 (1999), 52–75 | MR

[5] Kochetkov K. A., Shirkov P. D., “$L$-zatukhayuschie ROW metody tretego poryadka tochnosti”, Zh. vychisl. matem. i matem. fiz., 37:6 (1997), 699–710 | MR | Zbl

[6] Kochetkov K. A., Shirkov P. D., “$L$-zatukhayuschie ROW-metody s tochnoi otsenkoi lokalnoi pogreshnosti”, Matem. modelirovanie, 13:8 (2001), 38–43

[7] Shirkov P. D., “Ustoichivost ROW metodov dlya neavtonomnykh sistem obyknovennykh differentsialnykh uravnenii”, Matem. modelirovanie, 24:5 (2012), 97–111 | MR

[8] Shirkov P. D., “Optimalnye $L$-zatukhayuschie dvukhstadiinye skhemy Rozenbroka s kompleksnymi koeffitsientami dlya ODU”, Matem. modelirovanie, 4:8 (1992), 47–57 | MR | Zbl

[9] Limonov A. G., Alshin A. B., Alshina E. A., “Dvukhstadiinye kompleksnye skhemy Rozenbroka dlya zhestkikh sistem”, Zh. vychisl. matem. i matem. fiz., 49:2 (2009), 270–287 | MR | Zbl

[10] Zubanov A. M., Kokonkov N. I., Shirkov P. D., “Odnostadiinyi metod Rozenbroka s kompleksnymi koeffitsientami i avtomaticheskim vyborom shaga”, Matem. modelirovanie, 23:3 (2011), 127–138 | MR | Zbl

[11] Zubanov A. M., Shirkov P. D., “Metody tipa Rozenbroka, $L$-ekvivalentnye neyavnym metodam Runge–Kutty”, Fundamentalnye fiziko-matematicheskie problemy i modelirovanie tekhniko-tekhnologicheskikh sistem, Trudy 2-i Mezhdunarodnoi Konferentsii «Modelirovanie nelineinykh protsessov i sistem», Ezhegodnyi sbornik nauchnykh trudov, 14, ed. L. A. Uvarova, Yanus-K, M., 2011, 137–146

[12] Filippov S. S., “ABC-skhemy dlya zhestkikh sistem obyknovennykh differentsialnykh uravnenii”, Doklady RAN, 399:2 (2004), 170–172 | MR

[13] Kaps P., Roserbrock-type methods, Numerical method for solving stiff initial value problems, 9, eds. G. Dalhquist, R. Jeltsch, Inst. Fuer Geometrie und Praktische Math. Der RWTH Aachen, 1981

[14] Protero A., Robinson A., “On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations”, Math. of Comput., 28 (1974), 145–162 | DOI | MR

[15] Zubanov A. M., Shirkov P. D., “Dvukhstadiinye odnokratnye ROW metody s kompleksnymi koeffitsientami dlya avtonomnykh sistem ODU”, Kompyuternye issledovaniya i modelirovanie, Moskva, 2010, no. 1(2), 19–32