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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.
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