Implicit-Explicit Runge-Kutta-Rosenbrock Methods with Error Analysis for Nonlinear Stiff Differential Equations (Journal of Computational Mathematics, 2021)
Implicit-explicit Runge-Kutta-Rosenbrock methods are proposed to solve nonlinear stiffordinary 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 ofthe implicit-explicit methods are analysed. At last, some numerical examples are given toverify the validity of the obtained theoretical results and the effectiveness of the methods.