We present a positivity preserving numerical scheme for the pathwise solution of nonlinear stochastic differential equations driven by a multi-dimensional Wiener process and governed by non-commutative linear and non-Lipschitz vector fields. This strong order one scheme uses: (i) Strang exponential splitting, an approximation that decomposes the stochastic flow separately into the drift flow, a...

We prove a weak rate of convergence fully discrete scheme for stochastic Cahn--Hilliard equation with additive noise, where the spectral Galerkin method is used in space and backward Euler time. Compared Allen--Cahn type partial differential equation, error analysis here much more sophisticated due to presence unbounded operator front nonlinear term. To address such issues, novel direct approac...

In this study, the solutions of Simplified Magnetohyrodynamics (SMHD) equations by finite element method are examined with nonlinear time relaxation term. The differential filter κ(|u-u ̅ |(u-u )) term is added to SMHD equations. Also Nonlinear Time Relaxation Model (SMHDNTRM) introduced. model discretized Backward-Euler (BE) obtain solutions. Moreover, stability proved. found unconditionally st...

Influenced by Higham, Mao and Stuart [10], several numerical methods have been developed to study the strong convergence of the numerical solutions to stochastic differential equations (SDEs) under the local Lipschitz condition. These numerical methods include the tamed Euler–Maruyama (EM) method, the tamed Milstein method, the stopped EM, the backward EM, the backward forward EM, etc. In this ...

A discretization of an optimal control problem a stochastic parabolic equation driven by multiplicative noise is analyzed. The state discretized the continuous piecewise linear element method in space and backward Euler scheme time. convergence rate $$ O(\tau ^{1/2} + h^2) rigorously derived.

We show stability in a Banach space framework of backward Euler and second order backward diierence timestepping methods for a parabolic equation with memory. The results are applied to derive maximum norm stability estimates for piecewise linear nite element approximations in a plane spatial domain, which is accomplished by a new resolvent estimate for the discrete Laplacian. Error estimates a...

In this paper, we propose a class of discrete SIR epidemic models which are derived from SIR epidemic models with distributed delays by using a variation of the backward Euler method. Applying a Lyapunov functional technique, it is shown that the global dynamics of each discrete SIR epidemic model are fully determined by a single threshold parameter and the effect of discrete time delays are ha...

To avoid finding the stationary distributions of stochastic differential equations by solving the nontrivial Kolmogorov-Fokker-Planck equations, the numerical stationary distributions are used as the approximations instead. This paper is devoted to approximate the stationary distribution of the underlying equation by the Backward Euler-Maruyama method. Currently existing results [21, 31, 33] ar...

This paper discusses the relevant theoretical problem of the numerical derivative estimation of noisy signals. In this paper, a comparative study of some different schemes of the differentiators is given: Kalman filter, the well-known Super Twisting algorithm, Super Twisting with dynamic gains and Euler backward difference method. The analysis of the study results can focus on the strengths and...