Geodesic
Numerical integration of stiff systems with low accuracy
Matematičeskoe modelirovanie, Tome 22 (2010) no. 1, pp. 46-56.

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An L-stable (2,1)-method and an explicit two-stage Runge–Kutta type scheme are constructed, both schemes of order two. A numerical formula of order one is developed that is based on the stages of the explicit method and its stability interval is extended to 8. An integration algorithm of variable order and step is constructed that is based on the stages of the three schemes. The most effective numerical scheme is chosen for each step by means of stability control inequality. The results are given that confirm the effectiveness of the algorithm. 
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A. E. Novikov; E. A. Novikov. Numerical integration of stiff systems with low accuracy. Matematičeskoe modelirovanie, Tome 22 (2010) no. 1, pp. 46-56. http://geodesic.mathdoc.fr/item/MM_2010_22_1_a3/

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