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"Humanities and Science University Journal" №22 (Physical and mathematical, biological and technical science), 2016

Solving Problems of Moderate Stiffness Using Methods of the First Order with Conformed Stability Domains

M. V. Rybkov, A. E. Novikov, L. V. Knaub, P. S. Litvinov
Price: 50 руб.
 The Cauchy problem for a stiff system of ODEs is considered. Coeffi cients for stability polynomials of degree up to m = 27 are obtained. Corresponding explicit m-stage methods of the Runge-Kutta type of the fi rst order are designed with stability domains of intermediate numerical schemes conformed with the stability domain of the basic scheme. Inequalities for accuracy and stability control are obtained. Numerical results showing growth of the effi ciency are given.
Keywords: Runge-Kutta methods, accuracy and stability control, conformed stability 
domains, stiff problems.
REFERENCES
1. Hairer, E., & Wanner, G. Solving ordinary differential equations II. Stiff and 
differential-algebraic problems. 1996, USA: Springer-Verlag.
2. Novikov, E.A. Explicit methods for stiff systems [Явные методы для жестких 
систем]. 1997, Novosibirsk: Nauka.
3. Novikov, E.A., & Shornikov, Yu.V. Computer simulation of hybrid stiff systems 
[Компьютерное моделирование жестких гибридных систем]. 2012, Novosibirsk: 
NSTU.
4. Novikov, E.A. Design of stability domains of explicit methods of the Runge-Kutta 
type [Конструирование областей устойчивости явных методов типа Рунге-Кутта]. 
Computational Technologies and Programming, 2009, 10, 248–257.
5. Dahlquist, G.G. A special stability problem for linear multistep methods. BIT, 
1963, 3(1), 27–43. doi:10.1007/BF01963532
6. Novikov, E.A., & Rybkov, M.V. Numerical algorithm for design of stability 
domains of the fi rst order methods [Численный алгоритм построения многочленов 
устойчивости методов первого порядка]. Journal of Buryat State University, 2014, 
9(2), 80–85.
7. Novikov, A.E., & Novikov, E.A. Combined algorithm of the third order for solving 
stiff problems [Комбинированный алгоритм третьего порядка для решения жестких 
задач]. Computational Technologies, 2011, 16(6), 54–67.
8. Mazzia, F,. & Iavernaro, F. Test set for initial value problem solvers. 2003, Uni-
versity of Bari: Department of Mathematics.
Price: 50 рублей
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