Abstract In this paper, we discuss the construction of a class of implicit-explicit (IMEX) methods for systems of ordinary differential equations which their right hand side can be split into two parts; nonstiff or mildly stiff part and stiff part. The proposed methods treat the non-stiff part by an explicit second derivative diagonally implicit multistage integration method (SDIMSIM) and the stiff part by an implicit diagonally implicit multistage integration method (DIMSIM). The explicit part of these methods has strong stability preserving (SSP) property and the implicit part is A- and L-stable. We will construct methods with p = q = r = s and p = q + 1 = r = s up to order four with large SSP coefficients with respect to the large region of absolute stability, assuming that the implicit part of the method has Runge–Kutta stability (RKS) property together with A- and L-stability. These methods are tested on the linear advection-diffusion, advection-reaction and nonlinear shallow water equations, and the numerical results are presented conforming the efficiency and order of constructed methods.

中文翻译：

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具有强稳定性保留显式部分的变换隐显二阶导数对角隐式多级积分方法

摘要 在本文中，我们讨论了一类常微分方程组的隐显（IMEX）方法的构造，其中常微分方程组的右手边可以分为两部分；非刚性或轻度刚性部分和刚性部分。所提出的方法通过显式二阶导数对角隐式多级积分方法（SDIMSIM）处理非刚性部分，通过隐式对角隐式多级积分方法（DIMSIM）处理刚性部分。这些方法的显式部分具有很强的稳定性保持（SSP）特性，隐式部分是 A 和 L 稳定的。我们将构造具有 p = q = r = s 和 p = q + 1 = r = s 的方法，最多四阶，相对于绝对稳定的大区域，具有大的 SSP 系数，假设该方法的隐式部分具有龙格-库塔稳定性 (RKS) 特性以及 A 和 L 稳定性。这些方法在线性对流-扩散、对流-反应和非线性浅水方程上进行了测试，数值结果符合构造方法的效率和顺序。