This study investigates the frequency-dependence of fluid flow in heterogeneous porous media using the theory of dynamic penneability and a finite-difference method. Given a penneability distribution, the dynamic penneability is applied locally to calculate the frequency-dependence of fluid flow at each local point. An iterative Alternating Direction Implicit finite-difference technique is appl...

We propose a new high-order alternating direction implicit (ADI) finite difference scheme for the solution of initial-boundary value problems of convection-diffusion type with mixed derivatives and non-constant coefficients, as they arise from stochastic volatility models in option pricing. Our approach combines different high-order spatial discretisations with Hundsdorfer and Verwer’s ADI time...

A new method modifying the frequency dependent alternating direction implicit finite difference time domain (FD–ADI– FDTD) is presented. The method can improve the accuracy of FD–ADI–FDTD without significant increase of computational costs. The proposed method is validated by numerical tests. Index Terms ADI–FDTD, Debye media, Accuracy of FDTD

This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a highorder compact PRADI likemethod. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy,...

LOW-RANK ITERATIVE METHODS FOR PROJECTED GENERALIZED LYAPUNOV EQUATIONS TATJANA STYKEL Abstract. We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximat...

In this paper an analysis will be presented for the ADI (alternating direction implicit) method of Peaceman and Rachford applied to initial-boundary value problems for partial differential equations in two space dimensions. We shall use the method of lines approach. Motivated by developments in the field of stiff nonlinear ordinary differential equations, our analysis will focus on problems whe...

In this paper we propose a new projection method to solve large-scale continuous-time Lyapunov matrix equations. The new method projects the problem onto a much smaller approximation space, generated as a combination of Krylov subspaces in A and A. The reduced problem is then solved by means of a direct Lyapunov scheme based on matrix factorizations. The reported numerical results show the comp...

In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximu...

By J. Douglas, Jr., R. B. Kellogg, and R. S. Varga We consider the iterative solution of the system of linear equations (1 ) (Xi + X-, + • ■ ■ + Xn)z = /, n 2; 2, where each Xj, 1 | j | n, is a Hermitian and positive definite N X N matrix. If n = 2, the iterative methods of Peaceman-Rachford [1, Chapter 7], or D'yakonov [2] and Kellogg [3], may be used to solve (1). In this paper these methods ...

Abstract: We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractiona...