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

• 作者: Bin Huang Aiguo Xiao Gengen Zhang
• 来源期刊: 计算数学（英文版）
• 年，卷（期）: 2021,（4）
• 页码范围: 599-620
• 页数: 22页
• 语种: 英文
• DOI: 10.4208/jcm.2005-m2019-0238

摘要

Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear stiff ordinary differential equations by combining linearly implicit Rosenbrock methods with ex-plicit 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 condi-tion 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.