Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Space fractional diffusion equations with a nonlinear reaction term have been presented and used to model many problems of practical interest. In this paper, a two-dimensional Riesz space fractional diffusion equation with a nonlinear reaction term (2D-RSFDE-NR...

A dual transformation technique that can deal with awkward Coulomb potentials is developed for electronic wave packet dynamics. The technique consists of the variable transformation of the Hamiltonian and the transformation of the wave function with a normalization constraint. The time evolution is carried out by the alternating-direction implicit method. The operation of the transformed Hamilt...

We study accuracy of fractional time-stepping (FTS) methods such as the alternating direction implicit method for the computation of heat ows and the velocity-pressure splitting methods for Navier-Stokes ows. The FTS techniques can be viewed as a perturbation of conventional temporal-spatial discretization schemes; they in theory invoke a perturbation error that is on the same order as the disc...

The paper provides a set of algorithms for performing set operations on polygonal regions in the plane using standard floating-point arithmetc. The algorithms are robust, guaranteeing both topological consistency and numerical accuracy. Each polygon edge is modelled as an implicit or explicit polygonal curve which stays within some distance fl of the original line segment. If the curve is impli...

this study investigated the relative effects of deductive and inductive form-focused instruction (ffi) on the acquisition of 4 non-generic definite article uses(cultural, situational, structural, and textual) as assessed by explicit and implicit outcome measures. the tests utilized to assess efl learners' acquisition of definite article uses were timed and untimed grammaticality judgment tests....

The article provides a set of algorithms for performing set operations on polygonal regions in the plane using standard oating point arithmetic. The algorithms are robust, guaranteeing both topological consistency and numerical accuracy. Each polygon edge is modeled as an implicit or explicit polygonal curve which stays within some distance of the original line segment. If the curve is implicit...

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Itô form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order γ = 1 in the mean-square sense. The analysis of stability shows that the mean-square stability p...

this study investigated the relative effects of deductive and inductive form-focused instruction (ffi) on the acquisition of 4 non-generic definite article uses(cultural, situational, structural, and textual) as assessed by explicit and implicit outcome measures. the tests utilized to assess efl learners' acquisition of definite article uses were timed and untimed grammaticality judgment t...

Current methods for building models using implicit volume techniques present problems defining accurate and controllable blend shapes between implicit primitives. We present new methods to extend the freedom and controllability of implicit volume modeling. The main idea is to use a free-form curve to define the profile of the blend region between implicit primitives. The use of a free-form impl...

We theoretically study the behavior of He+ exposed simultaneously to an ultrashort intense Ti:sapphire laser and its 27th or 13th harmonic pulses, by solving the time-dependent Schrödinger equation using the alternating direction implicit method. This system is chosen as an interesting application of state-of-the-art high-order harmonic sources. Our results show that the simple hydrogenlike sys...