Stability and convergence analysis of stochastic Runge-Kutta and balanced stochastic Runge-Kutta methods for solving stochastic differential equations

This paper focuses on the utilization of the second-order Runge-Kutta method (SRKM) with balanced parameters (BSRKM). It begins by constructing a Butcher table that satisfies the second-order criteria. The authors then proceed to define balanced parameters for both random (BSRKM1) and nonrandom (BSRKM2) cases. The stability region and time step constraints for these cases are thoroughly examined and found to outperform the SRKM and other relevant studies. Furthermore, the convergence results demonstrate that the BSRKM methods exhibit lower mean absolute error (MAE) values, indicating a higher level of accuracy in approximating the solutions of both linear and nonlinear stochastic differential equations.