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Volume 39, Issue 4
Implicit-Explicit Runge-Kutta-Rosenbrock Methods with Error Analysis for Nonlinear Stiff Differential Equations

Bin Huang, Aiguo Xiao & Gengen Zhang

DOI: 10.4208/jcm.2005-m2019-0238

J. Comp. Math., 39 (2021), pp. 599-620.

Published online: 2021-05

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  • Abstract

Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear stiff ordinary differential equations by combining linearly implicit Rosenbrock methods with explicit Runge-Kutta methods. First, the general order conditions up to order 3 are obtained. Then, for the nonlinear stiff initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems, the corresponding errors of the implicit-explicit methods are analysed. At last, some numerical examples are given to verify the validity of the obtained theoretical results and the effectiveness of the methods.

  • Keywords

Stiff differential equations, Implicit-explicit Runge-Kutta-Rosenbrock method, Order conditions, Convergence.

  • AMS Subject Headings

65L04, 65L20, 65L06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huangbin_xtu@sina.com (Bin Huang)

xag@xtu.edu.cn (Aiguo Xiao)

zhanggen036@163.com (Gengen Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-599, author = {Huang , BinXiao , Aiguo and Zhang , Gengen}, title = {Implicit-Explicit Runge-Kutta-Rosenbrock Methods with Error Analysis for Nonlinear Stiff Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2021}, volume = {39}, number = {4}, pages = {599--620}, abstract = {

Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear stiff ordinary differential equations by combining linearly implicit Rosenbrock methods with explicit Runge-Kutta methods. First, the general order conditions up to order 3 are obtained. Then, for the nonlinear stiff initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems, the corresponding errors of the implicit-explicit methods are analysed. At last, some numerical examples are given to verify the validity of the obtained theoretical results and the effectiveness of the methods.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2005-m2019-0238}, url = {http://global-sci.org/intro/article_detail/jcm/19154.html} }
TY - JOUR T1 - Implicit-Explicit Runge-Kutta-Rosenbrock Methods with Error Analysis for Nonlinear Stiff Differential Equations AU - Huang , Bin AU - Xiao , Aiguo AU - Zhang , Gengen JO - Journal of Computational Mathematics VL - 4 SP - 599 EP - 620 PY - 2021 DA - 2021/05 SN - 39 DO - http://doi.org/10.4208/jcm.2005-m2019-0238 UR - https://global-sci.org/intro/article_detail/jcm/19154.html KW - Stiff differential equations, Implicit-explicit Runge-Kutta-Rosenbrock method, Order conditions, Convergence. AB -

Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear stiff ordinary differential equations by combining linearly implicit Rosenbrock methods with explicit Runge-Kutta methods. First, the general order conditions up to order 3 are obtained. Then, for the nonlinear stiff initial-value problems satisfying the one-sided Lipschitz condition and a class of singularly perturbed initial-value problems, the corresponding errors of the implicit-explicit methods are analysed. At last, some numerical examples are given to verify the validity of the obtained theoretical results and the effectiveness of the methods.

Huang , BinXiao , Aiguo and Zhang , Gengen. (2021). Implicit-Explicit Runge-Kutta-Rosenbrock Methods with Error Analysis for Nonlinear Stiff Differential Equations. Journal of Computational Mathematics. 39 (4). 599-620. doi:10.4208/jcm.2005-m2019-0238
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