Geodesic
An integration algorithm using the methods of Rosenbrock and Ceschino
Numerical methods and programming, Tome 14 (2013) no. 2, pp. 254-261 Cet article a éte moissonné depuis la source Math-Net.Ru

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An inequality for the stability control of Ceschino's scheme of second order of accuracy is constructed. Based on the stages of this method, a numerical formula of order one is developed whose stability interval is extended to 32. On the basis of the $L$-stable Rosenbrock scheme and the numerical Ceschino's formula, an algorithm of alternating structure in which an efficient numerical formula is chosen at every step according to a stability criterion is proposed. The algorithm is intended for solving stiff and nonstiff problems. Numerical results confirm the efficiency of this algorithm.
Keywords: stiff problems; Ceschino's scheme; Rosenbrock's method; accuracy and stability control. 
@article{VMP_2013_14_2_a4,
     author = {E. A. Novikov},
     title = {An integration algorithm using the methods of {Rosenbrock} and {Ceschino}},
     journal = {Numerical methods and programming},
     pages = {254--261},
     year = {2013},
     volume = {14},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2013_14_2_a4/}
}
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E. A. Novikov. An integration algorithm using the methods of Rosenbrock and Ceschino. Numerical methods and programming, Tome 14 (2013) no. 2, pp. 254-261. http://geodesic.mathdoc.fr/item/VMP_2013_14_2_a4/