In this paper, proper orthogonal decomposition (POD) is used for model reduction of mixed finite element (MFE) for the nonstationary Navier–Stokes equations and error estimates between a reference solution and the POD solution of reduced MFE formulation are derived. The basic idea of this reduction technique is that ensembles of data are first compiled from… (More)
—Based on the renowned additive operator splitting (AOS) schemes that ensure equal treatment of all coordinate axis, accelerated AOS schemes for solving regularized Perona-Malik (P-M) equation are presented. These ameliorated AOS schemes are stable unconditionally, consistent with nonlinear parabolic equations under certain circumstance and demonstrate a… (More)
Academic Editor: Feliz Manuel Minhós Copyright q 2011 Meiqiang Feng et al. 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. This paper is devoted to study the existence, nonexistence, and… (More)
In this paper, we present a regularization method to a degenerate variational inequality of parabolic type arising from American option pricing. Main difficulty in actually analyzing this kind of problem is caused by the presence of a non-smoothing initial value function in the formulation of the problem. We first use a smoothing technique with small… (More)
A coupled system, which consists of multiple delayed neural network loops, is proposed and a detailed analysis of the asymptotic behavior of the zero solution is included. The stable regions and all possible bifurcations, which depend on multiple parameters, are given in a geometrical way for several specific cases.
Black-Scholes equation is an important model in option pricing theory of financial, which is very practical in the application of numerical computation. In this paper, we construct a new kind of effective difference schemes (Explicit-Implicit scheme and Implicit-Explicit scheme) for solving option pricing model with transaction costs (Leland's model), give… (More)
Based on the renowned additive operator splitting (AOS) schemes that ensure equal treatment of all coordinate axes, accelerated AOS schemes for solving regularized Perona-Malik (P-M) equation are presented. These ameliorated AOS schemes are stable unconditionally, consistent with nonlinear parabolic equations under certain circumstance and… (More)