Geodesic
A fifth-order five-stage embedded method of the Dormand–Prince type
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1181-1191

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An explicit embedded method is examined for the numerical integration of a system of ordinary differential equations of a special form. Fifth-order five-stage numerical schemes with automatic step size selection are constructed for special systems of differential equations of the first and second orders. 
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     author = {I. V. Olemskoi},
     title = {A fifth-order five-stage embedded method of the {Dormand{\textendash}Prince} type},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1181--1191},
     publisher = {mathdoc},
     volume = {45},
     number = {7},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_7_a4/}
}
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I. V. Olemskoi. A fifth-order five-stage embedded method of the Dormand–Prince type. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 7, pp. 1181-1191. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_7_a4/