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This article is cited in 2 scientific papers (total in 2 papers)
Computational mathematics
An algorithm of variable structure based on three-stage explicit-implicit methods
A. E. Novikova, E. A. Novikovb, M. V. Rybkova a Siberian Federal University, Svobodny pr., 79/10, 660041, Krasnoyarsk, Russia
b Institute of computational modeling SB RAS, Akademgorodok, 50, str. 44, 660036, Krasnoyarsk, Russia
Abstract:
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, algorithm of variable structure.
Received March 5, 2017, published May 11, 2017
Citation:
A. E. Novikov, E. A. Novikov, M. V. Rybkov, “An algorithm of variable structure based on three-stage explicit-implicit methods”, Sib. Èlektron. Mat. Izv., 14 (2017), 433–442
Linking options:
https://www.mathnet.ru/eng/semr794 https://www.mathnet.ru/eng/semr/v14/p433
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