We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called direction and norm decomposition method, proposes to approximate the required solution $X_t$ by integrating the system of coupled SDEs that describes the evolution of the norm of $X_t$ and its projection on the unit sphere. This allows us to develop an explicit scheme for stiff SDEs with multiplicative noise that shows a solid performance in various numerical experiments. Under general conditions, the new integrator preserves the almost sure stability of the solutions for any step-size, as well as the property of being distant from $0$. The scheme also has linear rate of weak convergence for a general class of SDEs with locally Lipschitz coefficients,and one-half strong order of convergence.
Full moment error estimates in strong norms for numerical approximations of stochastic Navier-Stokes equations with multiplicative noise, Part I: time discretization
An efficient fully explicit scheme for stochastic Navier-Stokes equations driven by multiplicative noise
School of Mathematical Sciences, Xiamen university（厦门大学数学科学学院）；Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing, Xiamen University（福建省数学建模与高性能科学计算重点实验室）；School of Mathematics and Statistics, Guangdong University of Technology（广东工业大学数学与信息学院）
Two operator splitting methods for three-dimensional stochastic Maxwell equations with multiplicative noise
China University of Mining and Technology（中国矿业大学）；Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；Shanghai Zhangjiang Institute of Mathematics（上海张江数学研究院）
Energy-conserving method for Stochastic Maxwell Equations with Multiplicative Noise
Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；School of Mathematical Science, China University of Mining and Technology（中国矿业大学数学科学学院）；School of Mathematical Science, Huaiyin Normal University（淮阴师范学院数学科学学院）
Strong Convergence of a Stochastic Rosenbrock-type Scheme for the Finite Element Discretization of Semilinear SPDEs Driven by Multiplicative and Additive Noise
Strong convergence analysis of the stochastic exponential Rosenbrock scheme for the finite element discretization of semilinear SPDEs driven by multiplicative and additive noise
Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise
Umeå University（于默奥大学）；University of Innsbruck（因斯布鲁克大学）；Chalmers University of Technology and University of Gothenburg（查尔姆斯理工大学和哥德堡大学）；Central South University（中南大学）
Analysis of A Splitting Scheme for Damped Stochastic Nonlinear Schrödinger Equation with Multiplicative Noise
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Science, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
Galerkin finite element approximation for semilinear stochastic time-tempered fractional wave equations with multiplicative white noise and fractional Gaussian noise
