摘要
Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear sti ordinary di erential 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 sti 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 e ectiveness of the methods.
基金
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)
the Scientific Research Fund of Science and Technology Department of Hunan Province in China(Grant No.2018WK4006).