Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Fractional nonlinear reaction-diffusion models have found numerous applications in patten formation in biology, chemistry, physics and Engineering. Obtaining analytical solutions of fractional nonlinear reaction-diffusion models is difficult, generally numerica...

In this paper we consider the numerical solution of projected generalized continuous-time Lyapunov equations with low-rank right-hand sides. The interest in this problem stems from stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. Two projection methods are proposed for calculating low-rank approximate solutions. One is based ...

1. Introduction. In companion papers [l; 6] recently Peaceman, Rachford, and the author introduced a finite difference technique called therein the alternating direction implicit method for approximating the solution of transient and permanent heat flow problems in two space variables. The validity of the method was established only in the case of a rectangular domain. Since then the procedure ...

Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Abstract We discuss the numerical solution of large-scale sparse projected discrete-time periodic Lyapunov equations ...

The solution of large-scale Lyapunov equations is a crucial problem for several fields of modern applied mathematics, e. g., balanced truncation model order reduction. The low-rank version of the alternating directions implicit method (LR-ADI) is an iterative algorithm that computes approximate lowrank factors of the solution. In order to achieve a fast convergence it requires adequate shift pa...

in this paper, the temperature distribution around a moving heat source had been investigated including the phase change and non phase change . in non-phase change state, the governing equation was converted to finite difference equation by finite volume method and the equation was solved by alternating direction implicit method. this method was unconditionally stable . in phase change state, t...

Article history: Received 30 October 2009 Received in revised form 17 October 2010 Accepted 12 November 2010 Available online 19 November 2010

Article history: Received 9 July 2014 Accepted 19 August 2014 Available online xxxx

We consider the numerical solution of projected Lyapunov equations using Krylov subspace iterative methods. Such equations play a fundamental role in balanced truncation model reduction of descriptor systems. We present generalizations of the extended block and global Arnoldi methods to projected Lyapunov equations and compare these methods with the alternating direction implicit method with re...

although explicit and implicit knowledge of language learners are essential to theoretical and pedagogical debates in second language acquisition (sla), little research has addressed the effects of instructional interventions on the two knowledge types (r. ellis, 2005).this study examined the relative effectiveness of explicit and implicit types of form-focused instruction (ffi) on the acquisit...