We give a unified method to derive the strong convergence rate of backward Euler scheme for monotone SDEs in $L^p(\Omega)$-norm, with general $p \ge 4$. The results are applied SODEs polynomial growth coefficients. also generalize argument Galerkin-based SPDEs coefficients driven by multiplicative trace-class noise.

Abstract In this paper, we are concerned with the convergence rate of Euler–Maruyama (EM) scheme for stochastic differential delay equations (SDDEs) neutral type , where neutral, drift, and diffusion terms allowed to be polynomial growth. More precisely, SDDEs driven by Brownian motions, reveal that corresponding EM is one-half; Whereas pure jump processes, show best associated slower than one-...

Modern attitude and heading reference systems (AHRS) generally use Kalman Filter to integrate gyros with some other augmenting sensors, such as accelerometers and magnetometers, to provide a long term stable orientation solution. The construction of the Kalman Filter for the AHRS is flexible, while the general options are the methods based on quaternion, Euler angles, or Euler angle errors. But...

We generalise the current theory of optimal strong convergence rates for implicit Euler-based methods by allowing for Poisson-driven jumps in a stochastic differential equation (SDE). More precisely, we show that under one-sided Lipschitz and polynomial growth conditions on the drift coefficient and global Lipschitz conditions on the diffusion and jump coefficients, three variants of backward E...

In this study, a three-dimensional CFD transient model is established for predicting species concentration distribution in the biodegradation of phenol an airlift reactor (ALR). The gas–liquid flow ALR determined by Euler–Euler method coupled with standard k-? model, and bubble size predicted population balance (PBM). A turbulent mass diffusivity developed to simulate transfer process predict d...

Euler diagrams use closed curves to represent sets and their relationships. They facilitate set analysis, as humans tend to perceive distinct regions when closed curves are drawn on a plane. However, current automatic methods often produce diagrams with irregular, nonsmooth curves that are not easily distinguishable. Other methods restrict the shape of the curve to for instance a circle, but su...

We demonstrate the existence of solutions to the full 3 x 3 system of com-pressible Euler equations in one space dimension, up to an arbitrary time T > 0, in the case when the initial data has arbitrarily large total variation, and sufficiently small supnorm. The result applies to periodic solutions of the Euler equations, a nonlinear model for sound wave propagation in gas dynamics. Our analys...

We propose a new verification method to enclose solutions for initial value problems of systems of first-order nonlinear ordinary differential equations (ODEs) using a linearized inverse operator. The proposed approach can verify the existence and local uniqueness of the exact solution independent of the choice of the approximation scheme, while the existing methods usually depend on the numeri...