Stability Analysis of Numerical Schemes for Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Balanced Implicit Methods for Stiff Stochastic Systems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Implicit Taylor methods for stiff stochastic differential equations
Applied Numerical Mathematics
The composite Euler method for stiff stochastic differential equations
Journal of Computational and Applied Mathematics
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
SIAM Journal on Numerical Analysis
The fully implicit stochastic-α method for stiff stochastic differential equations
Journal of Computational Physics
Split-step forward methods for stochastic differential equations
Journal of Computational and Applied Mathematics
The composite Milstein methods for the numerical solution of Ito stochastic differential equations
Journal of Computational and Applied Mathematics
Physically consistent simulation of mesoscale chemical kinetics: The non-negative FIS-α method
Journal of Computational Physics
Asymptotic stability of balanced methods for stochastic jump-diffusion differential equations
Journal of Computational and Applied Mathematics
Split-step θ-method for stochastic delay differential equations
Applied Numerical Mathematics
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In this paper we discuss split-step backward balanced Milstein methods for solving Ito stochastic differential equations (SDEs). Four families of methods, a family of drifting split-step backward balanced Milstein (DSSBBM) methods, a family of modified split-step backward balanced Milstein (MSSBBM) methods, a family of drifting split-step backward double balanced Milstein (DSSBDBM) methods and a family of modified split-step backward double balanced Milstein (MSSBDBM) methods, are constructed in this paper. Their order of strong convergence is proved. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of stiff SDEs.