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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.