Implicit-Explicit Runge-Kutta-Rosenbrock Methods with Error Analysis for Nonlinear Stiff Differential Equations
Year: 2021
Author: Bin Huang, Aiguo Xiao, Gengen Zhang
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2005-m2019-0238
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 4 : pp. 599–620
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Stiff differential equations Implicit-explicit Runge-Kutta-Rosenbrock method Order conditions Convergence.
Author Details
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