Advanced Search

A new error correction method for the stationary Navier-Stokes equations based on two local Gauss integrations is presented. Applying the orthogonal projection technique, we introduce two local Gauss integrations as a stabilizing term in the error correction method, and derive a new error correction method. In both the coarse solution computation step and the error computation step, a locally stabilizing term based on two local Gauss integrations is introduced. The stability and convergence of the...

We study a third order singular boundary value problem with multi-point boundary conditions. Sufficient conditions are obtained for the existence of positive solutions of the problem. Recent results in the literature are significantly extended and improved. Our analysis is mainly based on a nonlinear alternative of Leray-Schauder.

A higher order pressure segregation scheme for the time-dependent incompressible magnetohydrodynamics (MHD) equations is presented. This scheme allows us to decouple the MHD system into two sub-problems at each time step. First, a coupled linear elliptic system is solved for the velocity and the magnetic field. And then, a Poisson-Neumann problem is treated for the pressure. The stability is analyzed and the error analysis is accomplished by interpreting this segregated scheme as a higher order...

The authors consider the boundary value problem with a two-parameter nonhomogeneous multi-point boundary condition $$\begin{array}{c}{u}^{\text{'}\text{'}}+g\left(t\right)f(t,u)=0,t\in (0,1),\\ u\left(0\right)=\alpha u\left(\xi \right)+\lambda ,u\left(1\right)=\beta u\left(\eta \right)+\mu .Criteriafortheexistenceofnontrivialsolutionsoftheproblemareestablished.Thenonlineartermf(t,x)maytakenegativevaluesandmaybeunboundedfrombelow.Conditionsaredeterminedbytherelationshipbetweenthebehavioroff(t,x)/xforxnear0and\pm \infty ,andthesmallestpositivecharacteristicvalueofanassociatedlinearintegraloperator.Theanalysismainlyreliesontopologicaldegreetheory.Thisworkcomplementssomerecentresultsintheliterature.Theresultsareillustratedwithexamples.\end{array}$$

In this paper, we propose a new economic dispatch model with random wind power, demand response and carbon tax. The specific feature of the demand response model is that the consumer's electricity demand is divided into two parts: necessary part and non-essential part. The part of the consumer's participation in the demand response is the non-essential part of the electricity consumption. The optimal dispatch objective is to obtain the minimum total cost (fuel cost, random wind power cost and emission...

In this paper, we study the existence of oscillatory and nonoscillatory solutions of neutral differential equations of the form $x\left(t\right)-cx(t-r)$’$P\left(t\right)x(t-\theta )-Q\left(t\right)x(t-\delta )$=0 where $c>0$, $r>0$, $\theta >\delta \ge 0$ are constants, and $P$, $Q\in C({ℝ}^{+},{ℝ}^{+})$. We obtain some sufficient and some necessary conditions for the existence of bounded and unbounded positive solutions, as well as some sufficient conditions for the existence of bounded and unbounded oscillatory solutions.

The synchronization of fractional-order complex networks with delay is investigated in this paper. By constructing a novel Lyapunov-Krasovskii function $V$ and taking integer derivative instead of fractional derivative of the function, a sufficient criterion is obtained in the form of linear matrix inequalities to realize synchronizing complex dynamical networks. Finally, a numerical example is shown to illustrate the feasibility and effectiveness of the proposed method.