数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (1): 65-74.doi: 10.1016/S0252-9602(10)60023-9

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CONVERGENCE ANALYSIS OF RUNGE-KUTTA METHODS FOR A CLASS OF RETARDED DIFFERENTIAL ALGEBRAIC SYSTEMS

肖飞雁, 张诚坚   

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • 收稿日期:2008-06-18 出版日期:2010-01-20 发布日期:2010-01-20
  • 基金资助:

    This work is supported by NSFC (10871078).

CONVERGENCE ANALYSIS OF RUNGE-KUTTA METHODS FOR A CLASS OF RETARDED DIFFERENTIAL ALGEBRAIC SYSTEMS

 XIAO Fei-Yan, ZHANG Cheng-Jian   

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
  • Received:2008-06-18 Online:2010-01-20 Published:2010-01-20
  • Supported by:

    This work is supported by NSFC (10871078).

摘要:

This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and  Lagrange interpolation. A new convergence concept, called $D_A$-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.

关键词: convergence, Runge-Kutta Methods, Lagrange interpolation,  , retarded differential algebraic systems

Abstract:

This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and  Lagrange interpolation. A new convergence concept, called $D_A$-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.

Key words: convergence, Runge-Kutta Methods, Lagrange interpolation,  , retarded differential algebraic systems

中图分类号: 

  • 65L05