Geodesic
Diagonally implicit Runge–Kutta FSAL methods for stiff and differential-algebraic systems
Matematičeskoe modelirovanie, Tome 14 (2002) no. 2, pp. 3-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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Implicit Runge-Kutta methods are considered which first stage coincides with the last stage of previous step. The methods of order 3, 4, 5 are proposed. Advantage of these methods in comparison with singly diagonally implicit Runge-Kutta methods is shown. 
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     title = {Diagonally implicit {Runge{\textendash}Kutta} {FSAL} methods for stiff and differential-algebraic systems},
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L. M. Skvortsov. Diagonally implicit Runge–Kutta FSAL methods for stiff and differential-algebraic systems. Matematičeskoe modelirovanie, Tome 14 (2002) no. 2, pp. 3-17. http://geodesic.mathdoc.fr/item/MM_2002_14_2_a0/

[1] Alexander R., “Diagonally implicit Runge-Kutta methods for stiff O.D.E.'s”, SIAM J. Numer. Anal., 14,:6 (1977), 1006–1021 | DOI | MR | Zbl

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

[3] Khairer E., Bonner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999

[4] Hosea M. E., Shampine L. F., “Analysis and implementation of TR-BDF2”, Applied Numerical Mathematics, 20:1–3 (1996), 21–37 | DOI | MR | Zbl

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

[6] Khairer E., Nersett S., Bonner G., Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Mir, M., 1990 | MR