Geodesic
Diagonally implicit Runge--Kutta FSAL methods for stiff and differential-algebraic systems
Matematičeskoe modelirovanie, Tome 14 (2002) no. 2, pp. 3-17

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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. 
@article{MM_2002_14_2_a0,
     author = {L. M. Skvortsov},
     title = {Diagonally implicit {Runge--Kutta} {FSAL} methods for stiff and differential-algebraic systems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--17},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2002_14_2_a0/}
}
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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/