Geodesic
Model equations for accuracy investigation of Runge--Kutta methods
Matematičeskoe modelirovanie, Tome 22 (2010) no. 5, pp. 146-160

Voir la notice de l'article provenant de la source Math-Net.Ru

The simplest equations are considered that simulate the behavior of various error components of Runge–Kutta methods. The expressions for the local and global errors are obtained. The minimization of these errors allows one to construct explicit and implicit methods that have an improved accuracy when solving stiff and differential-algebraic problems.
Keywords: Runge–Kutta methods, still problems, differential-algebraic problems, order reduction phenomen. 
@article{MM_2010_22_5_a13,
     author = {L. M. Skvortsov},
     title = {Model equations for accuracy investigation of {Runge--Kutta} methods},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {146--160},
     publisher = {mathdoc},
     volume = {22},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_5_a13/}
}
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L. M. Skvortsov. Model equations for accuracy investigation of Runge--Kutta methods. Matematičeskoe modelirovanie, Tome 22 (2010) no. 5, pp. 146-160. http://geodesic.mathdoc.fr/item/MM_2010_22_5_a13/