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...

Two approaches for approximating the solution of large-scale Lyapunov equations are considered: the alternating direction implicit (ADI) iteration and projective methods by Krylov subspaces. A link between them is presented by showing that the ADI iteration can always be identified by a Petrov-Galerkin projection with rational block Krylov subspaces. Then a unique Krylov-projected dynamical sys...

Jiang, H. and Y.S. Wong, A parallel alternating direction implicit preconditioning method, Journal of Computational and Applied Mathematics 36 (1991) 209-226. The alternating direction implicit (ADI) iterative method is an efficient iterative method to solve systems of linear equations due to its extremely fast convergence. The AD1 method has also been used successfully as a preconditioner in s...

This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. Th...

In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the sense of Caputo with order in (1, 2). The presented numerical scheme is based on the L2-1σ method in time and the Galerkin finite element method in space. The unconditional stability and ...

A novel formulation of approximate truncated balanced realization (TBR) is introduced to unify three approaches: two iterative methods for solving the underlying Lyapunov equations – the alternating directions implicit (ADI) iteration and the rational Krylov subspace method (RKSM) – and a two-step procedure that performs a Krylov-based projection and subsequently direct TBR. The framework allow...

sex in evolution Adi Livnat∗† ‡, Christos Papadimitriou ‡ , Jonathan Dushoff § and Marcus W. Feldman ¶ †Miller Institute for Basic Research in Science, University of California, Berkeley, CA 94720 USA,‡Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720 USA,§Department of Biology, McMaster University, Hamilton, ON L8S 4K1 CANADA, and ¶Departme...