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Статьи

"Humanities and Science University Journal" №10 (Physical and mathematical, biological and technical science), 2014.

An Algorithm of Variable Order and Step, Based on the Stages of the Dormand-Prince Method

E. A. Novikov, A. E. Novikov
Price: 50 руб.
 We have constructed an inequality for the stability control of the Dormand-Prince method of the eighth order of accuracy and a fi rst-order method with an enhanced stability region, based on the fi rst seven stages. There are given some numerical
results con fi rming the effi ciency increase due to alternating order using.
Keywords: stiff system, explicit methods, accuracy and stability control, algorithm of variable order and step.
REFERENCES
1. Novikov, E.A. Explicit methods for stiff systems. 1997, Russia: Nauka.
1. Hairer, E., Norsett, S.P., & Wanner, G. Solver ordinary differential equations.
Nonstiff problems. 1987, Germany: Springer-Verlag.
2. Hairer, E., & Wanner, G. Solver ordinary differential equations. Stiff and
differential algebraic problems. 1991, Germany: Springer-Verlag.
3. Novikov, E.A. Explicit methods for stiff systems. 1997, Russia: Nauka.
4. Novikov, E.A., & Shornikov, Yu.V. Computer simulation of stiff hybrid systems.
2012, Russia: publishing house NGTU.
5. Prince, P.J., & Dormand, J.R. High order embedded Runge-Kutta formulae.
J. Comp. Appl. Math., 1981, 7, 67–75.
Price: 50 рублей
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