Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Stability Analysis of Numerical Schemes for Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Numerical solutions of stochastic differential equations — implementation and stability issues
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Runge-Kutta methods for numerical solution of stochastic differential equations
Journal of Computational and Applied Mathematics
Weak Second Order Conditions for Stochastic Runge--Kutta Methods
SIAM Journal on Scientific Computing
Mean-Square and Asymptotic Stability of the Stochastic Theta Method
SIAM Journal on Numerical Analysis
Convergence and stability of the split-step θ-method for stochastic differential equations
Computers & Mathematics with Applications
Higher-order semi-implicit Taylor schemes for Itô stochastic differential equations
Journal of Computational and Applied Mathematics
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In a previous paper, we proposed the stochastic generalization of classical second-order two-stage explicit Runge-Kutta (RK) methods. The obtained stochastic schemes have second order in the weak sense. In this paper, the numerical stability of these RK schemes is studied. The study focuses on stability with respect to the second moment (MS-stability). Figures of the stability domains of the numerical schemes are shown. Numerical examples that confirm the theoretical results are also presented.