This article proposes and analyses distributed, leaderless, model-independent consensus algorithms for networked Euler–Lagrange systems. We propose a fundamental consensus algorithm, a consensus algorithm accounting for actuator saturation, and a consensus algorithm accounting for unavailability of measurements of generalised coordinate derivatives, for systems modelled by Euler–Lagrange equati...

We describe algorithms for estimating a given measure p known up to a constant of proportionality, based on a large class of diffusions (extending the Langevin model) for which p is invariant. We show that under weak conditions one can choose from this class in such a way that the diffusions converge at exponential rate to p, and one can even ensure that convergence is independent of the starti...

Copyright q 2012 J. Yang and Z. Zhuang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We rigorously justify a singular Euler-Poisson approximation of the incompressible Euler equations in the quasi-neutral regime for plasma phys...

A recently suggested method for absorbing boundary conditions for the Euler equations is examined. The method is of PML type and has the important property of being well posed. Results from numerical experiments using a second order discretization are presented. For some choices of parameters the method becomes unstable. The instability is observed to originate from the corner regions. A modifi...

Mud volcanoes are taken into consideration by geologists and oil industry experts have given their association with oil and gas reserves and methane greenhouse gas production in hydrosphere and atmosphere. Gomishan mud volcano phenomenon in the southeastern edge of the Caspian Sea, given its oil and gas resources, has been studied by some geologists in terms of geology and tectonics but not in ...

We establish the validity of Euler$+$Prandtl approximation for solutions Navier-Stokes equations in half plane with Dirichlet boundary conditions, vanishing viscosity limit, initial data which are analytic only near boundary, and Sobolev smooth away from boundary. Our proof does not require higher order correctors, works directly by estimating an $L^{1}$-type norm vorticity error term expansion...

Several nonlinear Black-Scholes models have been proposed to take transaction cost, large investor performance and illiquid markets into account. One of the most comprehensive models introduced by Barles and Soner in [4] considers transaction cost in the hedging strategy and risk from an illiquid market. In this paper, we compare several finite difference methods for the solution of this model ...

We consider the fixed and exponential time-stepping Euler algorithms, with boundary tests, to calculate the mean first exit times (MFET) of two one-dimensional neural diffusion models, represented by the Ornstein–Uhlenbeck (OU) process and a stochastic space-clamped FitzHugh–Nagumo (FHN) system. The numerical methods are described and the convergence rates for the MFET analysed. A boundary test...

We perform an error analysis for numerical approximation methods of continuous time Markov chain models commonly found in the chemistry and biochemistry literature. The motivation for the analysis is to be able to compare the accuracy of different approximation methods and, specifically, Euler tau-leaping and midpoint tau-leaping. We perform our analysis under a scaling in which the size of the...