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...

Temperature decay in an aluminium plate is observed using Galerkin finite element method for 2D transient heat conduction equation. Taking ∆t of 0.001 hr , temperature variation is studied using unconditionally stable first order and second order accurate schemes backward Euler and modified CrankNicholson respectively. A comparative study has been made taking different combinations of meshes an...

The linearized Cahn-Hilliard-Cook equation is discretized in the spatial variables by a standard finite element method. Strong convergence estimates are proved under suitable assumptions on the covariance operator of the Wiener process, which is driving the equation. The backward Euler time stepping is also studied. The analysis is set in a framework based on analytic semigroups. The main part ...