The paper aims to obtain the convergence and mean-square (M.S.) stability analysis of the 1.5 strong-order stochastic Runge–Kutta (SRK) methods for the It\(\hat{ o}\) multi-dimensional stochastic linear scalar with one-dimensional noise term and additive test differential equations. The stability region of the proposed methods is compared to other SRK methods in Rößler (SIAM J Numer Anal 48(3):922–952, 2010). The proposed methods are used to increase the efficiency of the existing methods and to reduce the computational complexity when compared with the other existing SRK methods. Through numerical experiments, the convergence and M.S. stability of the 1.5 strong-order SRK methods show that the proposed methods are more efficient than the existing SRK methods.

本文旨在获得一维It \（\ hat {o} \）多维随机线性标量的1.5强阶随机Runge-Kutta（SRK）方法的收敛性和均方（MS）稳定性分析。维噪声项和加性检验微分方程。在Rößler中，将所提出方法的稳定性区域与其他SRK方法进行了比较（SIAM J Numer Anal 48（3）：922–952，2010）。与其他现有的SRK方法相比，所提出的方法可提高现有方法的效率并降低计算复杂度。通过数值实验，1.5种强阶SRK方法的收敛性和MS稳定性表明，所提出的方法比现有的SRK方法更有效。