We introduce a class of implicit–explicit (IMEX) schemes for the numerical solution of initial value problems of differential equations with both non-stiff and stiff components in which non-stiff and stiff solvers are, respectively, based on the explicit general linear methods (GLMs) and implicit second derivative GLMs (SGLMs). The order conditions of the proposed IMEX schemes are obtained. Linear stability properties of the methods are analyzed and then methods up to order four with a large area of absolute stability region of the pair are constructed assuming that the implicit part of the methods is L-stable. Due to the high stage orders of the constructed methods, they are not marred by order reduction. This is verified by the numerical experiments which demonstrate the efficiency of the proposed methods, too.

中文翻译：

---

隐式-显式二阶导数对角隐式多级积分法

对于具有非刚性和刚性分量的微分方程初值问题的数值解，我们引入了一类隐式-显式（IMEX）方案，其中，非刚性和刚性求解器分别基于显式通用线性方法（GLM）和隐式二阶导数GLM（SGLM）。获得了建议的IMEX方案的订购条件。分析方法的线性稳定性，然后在假设方法的隐式部分为L的情况下，构造该方法对中具有大对绝对稳定性区域的四阶方法。-稳定。由于所构造方法的高阶订单，因此它们不会因订单减少而受到损害。数值实验验证了这一点，该数值实验也证明了所提出方法的有效性。