Geodesic
An algorithm of variable structure based on three-stage explicit-implicit methods
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 433-442

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An explicit three-stage Runge–Kutta type scheme and L-stable Rosenbrock method are derived, both schemes of order 3. A numerical formula of order 1 is developed on the base of the stages of the explicit third order method. The stability interval of the first order formula is extended up to 18. The integration algorithm of variable order and step is constructed on the base of these three schemes. For each integration step the most efficient numerical scheme is chosen using an inequality for stability control. Numerical results confirming efficiency of the algorithm are given.
Keywords: stiff problem, one-step method, accuracy and stability control
Mots-clés : algorithm of variable structure. 
@article{SEMR_2017_14_a105,
     author = {A. E. Novikov and E. A. Novikov and M. V. Rybkov},
     title = {An algorithm of variable structure based on three-stage explicit-implicit methods},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {433--442},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a105/}
}
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A. E. Novikov; E. A. Novikov; M. V. Rybkov. An algorithm of variable structure based on three-stage explicit-implicit methods. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 433-442. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a105/