An efficient scheme for the implementation of implicit Runge-Kutta methods

被引：0
作者：
L. M. Skvortsov
机构：
[1] Bauman State Technical University,
来源：
Computational Mathematics and Mathematical Physics | 2008年 / 48卷
关键词：
implicit Runge-Kutta methods; modified Newton’s iteration; starting values; stiffness;
D O I：
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学科分类号：
摘要：
A scheme is proposed for solving nonlinear algebraic equations arising in the implementation of the implicit Runge-Kutta methods. In contrast to the available schemes, not only the starting values of the variables but also those of the derivatives are predicted. This makes it possible to reduce the number of evaluations of the function (the right-hand side) at each implicit stage without significantly reducing the accuracy of integration.
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页码：2007 / 2017
页数：10
相关论文
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  • [1] Kulikov G. Yu.(1998)Numerical Solution of the Cauchy Problem for a System of Differential-Algebraic Equations with the Use of Implicit Runge-Kutta Methods with a Nontrivial Predictor Zh. Vychisl. Mat. Mat. Fiz. 38 68-84
  • [2] Olsson H.(1998)Stage Value Predictors and Efficient Newton Iterations in Implicit Runge-Kutta Methods SIAM J. Sci. Comput. 20 185-202
  • [3] Söderlind G.(1999)IRK Methods for DAE: Starting Algorithms J. Comput. Appl. Math. 111 77-92
  • [4] Roldan T.(2000)Starting Algorithms for Some DIRK Methods Numer. Algorithms 23 357-369
  • [5] Higueras I.(2000)On the Starting Algorithms for Fully Implicit Runge-Kutta Methods BIT 40 685-714
  • [6] Higueras I.(2001)On the Implementation of ESIRK Methods for Stiff IVPs Numer. Algorithms 26 201-218
  • [7] Roldan T.(2003)Variable-Order Starting Algorithms for Implicit Runge-Kutta Methods on Stiff Problems Appl. Numer. Math. 44 77-94
  • [8] Gonzalez-Pinto S.(2003)IRK Methods for Index 2 and 3 DAEs: Starting Algorithms BIT 43 67-92
  • [9] Montijano J. I.(2003)Two-Step High Order Starting Values for Implicit Runge-Kutta Methods Adv. Comput. Math. 19 401-412
  • [10] Perez-Rodriguez S.(2004)Are High Order Variable Step Equistage Initializers Better Than Standard Starting Algorithms? J. Comput. Appl. Math. 169 333-344
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