In this paper we describe the construction of second derivative general linear method with Runge–Kutta stability property preserving the strong stability properties of spatial discretizations. Then we present such methods that are obtained by the solution of the constrained minimization problem with nonlinear inequality constraints, corresponding to the strong stability preserving property of these methods, and equality constraints, corresponding to the order, stage order and Runge–Kutta stability conditions. The derived methods are of order \(p=q\) with \(r=2\) and \(s=p\) or \(s=p+1\), of order \(p=q=s=r-1\) and of order \(p=q+1=s=r\), where q, s and r are the stage order, the number of internal and the number of external stages, respectively. Efficiency of the proposed methods together with verification of the order of convergence and capability of these methods in solving partial differential equations with smooth and discontinues initial data are shown by some numerical experiments.

在本文中，我们描述了具有Runge–Kutta稳定性的二阶导数一般线性方法的构造，该方法保留了空间离散化的强稳定性。然后，我们提出了这样的方法，这些方法是通过求解带有非线性不等式约束的约束最小化问题而获得的，这些约束对应于这些方法的强稳定性保持性质，而等式约束则对应于阶次，阶段次序和龙格－库塔稳定条件。派生方法的顺序为\（p = q \）和\（r = 2 \）和\（s = p \）或\（s = p + 1 \），顺序为\（p = q = s = r-1 \）并具有\（p = q + 1 = s = r \）的阶，其中q，s和r分别是阶段顺序，内部阶段数和外部阶段数。一些数值实验表明，所提方法的有效性以及对收敛顺序的验证以及这些方法在求解具有光滑初始和不连续初始数据的偏微分方程中的能力。