Geodesic
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.

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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. 
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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