One-step approximations for stochastic functional differential equations
Applied Numerical Mathematics
Improved linear multi-step methods for stochastic ordinary differential equations
Journal of Computational and Applied Mathematics
SDELab: A package for solving stochastic differential equations in MATLAB
Journal of Computational and Applied Mathematics
Mean-square convergence of stochastic multi-step methods with variable step-size
Journal of Computational and Applied Mathematics
One-step approximations for stochastic functional differential equations
Applied Numerical Mathematics
Mathematics and Computers in Simulation
Stochastic Runge-Kutta Methods for Itô SODEs with Small Noise
SIAM Journal on Scientific Computing
Runge-Kutta methods for jump-diffusion differential equations
Journal of Computational and Applied Mathematics
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A new approach to the construction of mean-square numerical methods for the solution of stochastic differential equations with small noises is proposed. The approach is based on expanding the exact solution of the system with small noises in powers of time increment and small parameter. The theorem on the mean-square estimate of method errors is proved. Various efficient numerical schemes are derived for a general system with small noises and for systems with small additive and small colored noises. The proposed methods are tested by calculation of Lyapunov exponents and simulation of a laser Langevin equation with multiplicative noises.