We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an alternative direction implicit (ADI) splitting method for its numerical solution. To treat the high-order and mixed derivative terms in the equation we adopt an ADI method by Hundsdorfer and Verwer to the present setting. The paper is furnished with numerical results for the evolut...

The completion mode (individual, collaborative) of the tasks and the conditions under which these modes are performed have been reported to play an important role in language learning. The present study aimed to investigate the effects of employing text editing tasks performed both individually and collaboratively, on the achievement of English grammar under explicit and implicit learning condi...

We present an extrapolative model of bubbles. In the model, many investors form their demand for a risky asset by weighing two signals—an average of the asset’s past price changes and the asset’s degree of overvaluation. The two signals are in conflict, and investors “waver” over time in the relative weight they put on them. The model predicts that good news about fundamentals can trigger large...

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal i...

We present a multilevel high order ADI method for separable generalized Helmholtz equations. The discretization method we use is a 1-D fourth order compact nite di erence applied to each directional component of the Laplace operator, resulting a discrete system e ciently solvable by ADI methods. We apply this high order di erence scheme to all levels of grids, and then starting from the coarses...

introduction: the aim of this study was to assess of both implicit and explicit motor sequence learning in children with attention deficit hyper activity disorder (adhd) and typical peers , by serial reaction time task. materials and methods: the sample size for each group was 12. the study sample was included 24 children with adhd, in explicit learning group and implicit learning group.  and 2...

A unified method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated SemiLagrangian advection algorithm is presented. The deforming material boundaries are represented using the moment-of-fluid method. The new algorithm uses a semi-implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection meth...

Semi-Lagrangian (S-L for short) methods, also called quasi-Lagrangian, have been around since the early 1960’s. T.N. Krishnamurti is probably the first to use S-L method. The S-L scheme becomes really popular following Andre Robert’s work in the early 80’s (Robert 1982) when he combined the use of S-L with semi-implicit method (SLSI) which allows for large time step size because both schemes ar...

Convection-diffusion equations are widely used for modeling and simulations of various complex phenomena in science and engineering (Hundsdorfer & Verwer, 2003; Morton, 1996). Since for most application problems it is impossible to solve convection-diffusion equations analytically, efficient numerical algorithms are becoming increasingly important to numerical simulations involving convection-d...

Fractional order diffusion equations are generalizations of classical diffusion equations which are used to model in physics, finance, engineering, etc. In this paper we present an implicit difference approximation by using the alternating directions implicit (ADI) approach to solve the two-dimensional space-time fractional diffusion equation (2DSTFDE) on a finite domain. Consistency, unconditi...