IMPLICIT-EXPLICIT RUNGE-KUTTA-ROSENBROCK METHODS WITH ERROR ANALYSIS FOR NONLINEAR STIFF DIFFERENTIAL EQUATIONS

doi:10.4208/jcm.2005-m2019-0238

Journal of Computational Mathematics ›› 2021, Vol. 39 ›› Issue (4): 599-620.DOI: 10.4208/jcm.2005-m2019-0238

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IMPLICIT-EXPLICIT RUNGE-KUTTA-ROSENBROCK METHODS WITH ERROR ANALYSIS FOR NONLINEAR STIFF DIFFERENTIAL EQUATIONS

Bin Huang¹, Aiguo Xiao¹, Gengen Zhang²

1 School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan 411105, China;
2 South China Research Center for Applied Mathematics and Interdisciplinary Studies, South China Normal University, Guangzhou 510631, China

Received:2019-10-25 Revised:2020-02-12 Online:2021-07-15 Published:2021-08-06
Contact: Gengen Zhang,Email:zhanggen036@163.com
Supported by:
The authors wish to thank the anonymous referees for their valuable comments and suggestions. The work is supported by the National Natural Science Foundation of China (Grant Nos. 11671343, 11701110), the Foundation for the Key Laboratory of Computational Physics, China (No. 6142A05180103) as well as the Scientific Research Fund of Science and Technology Department of Hunan Province in China (Grant No. 2018WK4006).

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Bin Huang, Aiguo Xiao, Gengen Zhang. IMPLICIT-EXPLICIT RUNGE-KUTTA-ROSENBROCK METHODS WITH ERROR ANALYSIS FOR NONLINEAR STIFF DIFFERENTIAL EQUATIONS[J]. Journal of Computational Mathematics, 2021, 39(4): 599-620.

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.

Key words: Stiff differential equations, Implicit-explicit Runge-Kutta-Rosenbrock method, Order conditions, Convergence

CLC Number:

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IMPLICIT-EXPLICIT RUNGE-KUTTA-ROSENBROCK METHODS WITH ERROR ANALYSIS FOR NONLINEAR STIFF DIFFERENTIAL EQUATIONS

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