Geodesic
On symmetry of some Runge--Kutta methods
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 4, pp. 1131-1140

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In the paper we investigate the property of symmetry for Runge–Kutta methods. We prove that methods possessing such property are fully implicit, and they can be constructed by the Gauss and Lobatto quadrature formulas. But only the Gauss formulas give algebraically stable Runge–Kutta methods. 
@article{FPM_2000_6_4_a11,
     author = {G. Yu. Kulikov},
     title = {On symmetry of some {Runge--Kutta} methods},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1131--1140},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_4_a11/}
}
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G. Yu. Kulikov. On symmetry of some Runge--Kutta methods. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 4, pp. 1131-1140. http://geodesic.mathdoc.fr/item/FPM_2000_6_4_a11/