Mean-square stability of 1.5 strong convergence orders of diagonally drift Runge–Kutta methods for a class of stochastic differential equations

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 Ito^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{ o}$$\end{document} 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.