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 - <p style="text-align: justify;">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.</p>