This article is cited in 2 scientific papers (total in 2 papers)
One-stage Rosenbrock method with complex coefficients and automatic time step evaluation
A. M. Zubanova, N. I. Kokonkovb, P. D. Shirkovc
a Dubna International University for Nature, Society, and Man
b Moscow Institute of Physics and Technology
c Dubna International University of Nature, Society and Man (Dmitrov Branch)
Well-known one-stage Rosenbrock scheme with complex coefficients is generalized to the case which allows to make a simple estimation of the truncation error. New version of such a scheme preserves all properties of the old one (such as $A$-stability and $L$-decrementation) and makes possible to choose step of integration automatically with the use of correction procedure.
Testing of strategy of time step evaluation as well as of new method has been done with the use of well known and original nonlinear differential equations and systems of equations include nonlinear equation of the heat conduction.
Rosenbrock methods, monotonous schemes, stiff problems, method of lines, automatic time step evaluation.
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Mathematical Models and Computer Simulations, 2011, 3:5, 596–603
A. M. Zubanov, N. I. Kokonkov, P. D. Shirkov, “One-stage Rosenbrock method with complex coefficients and automatic time step evaluation”, Matem. Mod., 23:3 (2011), 127–138; Math. Models Comput. Simul., 3:5 (2011), 596–603
Citation in format AMSBIB
\by A.~M.~Zubanov, N.~I.~Kokonkov, P.~D.~Shirkov
\paper One-stage Rosenbrock method with complex coefficients and automatic time step evaluation
\jour Matem. Mod.
\jour Math. Models Comput. Simul.
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A. M. Zubanov, P. D. Shirkov, “Numerical study of one-step lineary implicit methods which are L-equivalent to stiffly accurate two-stages Runge–Kutta schemes”, Math. Models Comput. Simul., 5:4 (2013), 350–355
A. M. Zubanov, N. N. Kutrukhin, P. D. Shirkov, “O postroenii lineino neyavnykh skhem, $LN$-ekvivalentnykh neyavnym metodam Runge–Kutty”, Kompyuternye issledovaniya i modelirovanie, 4:3 (2012), 483–496
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