Lijin Wang

Predictor-corrector methods for a linear stochastic oscillator with additive noise

The predictor-corrector methods P(EC)^k with equidistant discretization are applied to the numerical integration of a linear stochastic oscillator. Their ability in preserving the symplecticity, the linear growth property of the second moment, and the oscillation property of the solution of this stochastic system is studied. Their mean-square orders of convergence are discussed. Numerical experiments are performed.

Computational singular perturbation analysis of stochastic chemical systems with stiffness

Abstract Computational singular perturbation (CSP) is a useful method for analysis, reduction, and time integration of stiff ordinary differential equation systems. It has found dominant utility, in particular, in chemical reaction systems with a large range of time scales at continuum and deterministic level. On the other hand, CSP is not directly applicable to chemical reaction systems at micro or meso-scale, where stochasticity plays an non-negligible role and thus has to be taken into account. In this work we develop a novel stochastic computational singular perturbation (SCSP) analysis and time integration framework, and associated algorithm, that can be used to not only construct accurately and efficiently the numerical solutions to stiff stochastic chemical reaction systems, but also analyze the dynamics of the reduced stochastic reaction systems. The algorithm is illustrated by an application to a benchmark stochastic differential equation model, and numerical experiments are carried out to demonstrate the effectiveness of the construction.

Effective Computation of Stochastic Protein Kinetic Equation by Reducing Stiffness via Variable Transformation

The stochastic protein kinetic equations can be stiff for certain parameters, which makes their numerical simulation rely on very small time step sizes, resulting in large computational cost and accumulated round-off errors. For such situation, we provide a method of reducing stiffness of the stochastic protein kinetic equation by means of a kind of variable transformation. Theoretical and numerical analysis show effectiveness of this method. Its generalization to a more general class of stochastic differential equation models is also discussed.

A new symplectic method for a linear stochastic oscillator via stochastic variational integrators

n this manuscript, we apply the stochastic variational integrators theory to a linear stochastic oscillator, to construct a new symplectic scheme via a different discretization of the stochastic action integral. Numerical tests show efficiency, as well as the second order mean-square convergence of the scheme.

The third kind of generating functions of stochastic symplectic integrators

In this paper, we investigate the third kind of generating functions for constructing symplectic numerical methods for stochastic Hamiltonian systems. This kind of generating functions are compared with the first kind of generating functions which are more studied in literature. Superiorities of them are shown via some theoretical and empirical analysis.

Stochastic multisymplectic integrator for stochastic KdV equation

In this paper we investigate the stochastic multisymplectic methods to solve the stochastic partial differential equation. The stochastic KdV equations are considered. Besides conserving the multi-symplectic structure of original equation, the stochastic multi-symplectic methods are also investigated for the conservation of various conservation laws. We deduce the transit laws of the specific formal conservation laws. Numerical experiments are illustrated to verify the good behaviors of stochastic multisymplectic methods.