Geodesic
Algorithm variable order, step and the configuration variables for solving stiff problems
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 3, pp. 35-43

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An inequality for stability control of a Ceschino's scheme of second order of accuracy is constructed. A numerical formula of order one is developed that is based on the stages of the this method and its stability interval is extended to 32. On a base of $L$-stable $(2,1)$-scheme and a numerical Ceschino's formula, an algorithm of alternating structure, in which an efficient numerical formula is chosen on an every step by a stability criterion, is constructed. The algorithm is intended for solving stiff and non-stiff problems. There are shown results of calculations, confirming efficiency of this algorithm. 
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     author = {E. A. Novikov},
     title = {Algorithm variable order, step and the configuration variables for solving stiff problems},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {35--43},
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     url = {http://geodesic.mathdoc.fr/item/ISU_2013_13_3_a4/}
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E. A. Novikov. Algorithm variable order, step and the configuration variables for solving stiff problems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 3, pp. 35-43. http://geodesic.mathdoc.fr/item/ISU_2013_13_3_a4/