diagonally drift balanced stochastic runge–kutta methods of second-order for stochastic differential system of equations

In this paper, we investigate the mean square stability analysis of the secondorder balanced stochastic runge–kutta methods for scalar (bsrkms) stochastic differentialequations. for which we design a three-stages butcher table so that it condition for weakconvergence of the second-order runge-kutta applies. using the spectral radius of the matrixs, we plot the convergence region when x → −∞ and y → 0. the control function improvesthe stability conditions. we obtain the stability region with and without control function,we also draw the stability region for different control functions.keywords: scalar stochastic differential equations, balanced stochastic runge–kutta methods,mean-square stability, control functions for numerical schemes.