Geodesic
Algorithm of integrating stiff problems using the explicit and implicit methods
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 4, pp. 19-27

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An $L$-stable $(3,2)$-method order 3 and an explicit three-stage Runge–Kutta scheme order 1 are constructed. An integration algorithm of variable order and step is constructed that is based on of the two schemes The most effective numerical scheme is chosen for each step by means of stability control. The results are given that confirm the effectiveness of the algorithm. 
@article{ISU_2012_12_4_a3,
     author = {E. A. Novikov},
     title = {Algorithm of integrating stiff problems using the explicit and implicit methods},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {19--27},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2012_12_4_a3/}
}
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E. A. Novikov. Algorithm of integrating stiff problems using the explicit and implicit methods. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 4, pp. 19-27. http://geodesic.mathdoc.fr/item/ISU_2012_12_4_a3/