Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems

被引：2
|
作者：
Yue, Chao [1 ,2 ,3 ]
Xiao, Aiguo [1 ,2 ]
Liu, Hongliang [1 ,2 ]
机构：
[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Peoples R China
[2] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Peoples R China
[3] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
来源：
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS | 2015年 / 7卷 / 04期
关键词：
Stiff problem; additive Runge-Kuttamethod; implicit-explicitmethod; B-convergence; algebraic stability; SCHEMES; CONVECTION; ORDER;
D O I：
10.4208/aamm.2013.m230
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we are devoted to nonlinear stability and B-convergence of additive Runge-Kutta (ARK) methods for nonlinear stiff problems with multiple stiffness. The concept of (theta, p(-), q(-))-algebraic stability of ARK methods for a class of stiff problems K-sigma,K-tau is introduced, and it is proven that this stability implies some contractive properties of the ARK methods. Some results on optimal B-convergence of ARK methods for K-sigma,K-0 are given. These new results extend the existing ones of RK methods and ARK methods in the references. Numerical examples test the correctness of our theoretical analysis.
引用
收藏
页码：472 / 495
页数：24
相关论文
共 50 条
  • [41] B-STABILITY OF THE METHODS OF RUNGE-KUTTA
    CROUZEIX, M
    NUMERISCHE MATHEMATIK, 1979, 32 (01) : 75 - 82
  • [42] Runge-Kutta methods for affinely controlled nonlinear systems
    Kloeden, Peter E.
    Rossler, Andreas
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 205 (02) : 957 - 968
  • [43] A-stable Explicit Nonlinear Runge-Kutta Methods
    曹阳
    李庆扬
    Tsinghua Science and Technology, 1998, (04) : 1227 - 1232
  • [44] Explicit Runge-Kutta Methods for Stiff Problems with a Gap in Their Eigenvalue Spectrum
    Bocher, Philippe
    Montijano, Juan, I
    Randez, Luis
    Van Daele, Marnix
    JOURNAL OF SCIENTIFIC COMPUTING, 2018, 77 (02) : 1055 - 1083
  • [45] Some Optimal Runge-Kutta Collocation Methods for Stiff Problems and DAEs
    Gonzalez-Pinto, S.
    Hernandez-Abreu, D.
    Montijano, J. I.
    NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, 2008, 1048 : 880 - +
  • [46] Implicit-explicit Runge-Kutta methods for stiff combustion problems
    Lindblad, E.
    Valiev, D. M.
    Muller, B.
    Rantakokko, J.
    Lotstedt, P.
    Liberman, M. A.
    SHOCK WAVES, VOL 1, PROCEEDINGS, 2009, : 299 - +
  • [47] B-convergence of general linear methods for stiff problems
    Huang, CM
    Chang, QS
    Xiao, AG
    APPLIED NUMERICAL MATHEMATICS, 2003, 47 (01) : 31 - 44
  • [48] Nonlinear stability of natural Runge-Kutta methods for neutral delay differential equations
    Zhang, CJ
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2002, 20 (06) : 583 - 590
  • [49] Hα-stability of modified Runge-Kutta methods for nonlinear neutral pantograph equations
    Ma, S. F.
    Yang, Z. W.
    Liu, M. Z.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 335 (02) : 1128 - 1142
  • [50] Input-to-state stability of Runge-Kutta methods for nonlinear control systems
    Hu, Guang-Da
    Liu, Mingzhu
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 205 (01) : 633 - 639
12345