Geodesic
Runge–Kutta collocation methods for differential-algebraic equations of indices 2 and 3
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 10, pp. 1801-1811

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Stiffly accurate Runge–Kutta collocation methods with explicit first stage are examined. The parameters of these methods are chosen so as to minimize the errors in the solutions to differential-algebraic equations of indices 2 and 3. This construction results in methods for solving such equations that are superior to the available Runge–Kutta methods. 
@article{ZVMMF_2012_52_10_a4,
     author = {L. M. Skvortsov},
     title = {Runge{\textendash}Kutta collocation methods for differential-algebraic equations of indices~2 and~3},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1801--1811},
     publisher = {mathdoc},
     volume = {52},
     number = {10},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_10_a4/}
}
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L. M. Skvortsov. Runge–Kutta collocation methods for differential-algebraic equations of indices 2 and 3. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 10, pp. 1801-1811. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_10_a4/