An efficient modification by Douglas and Kim of the usual alternating directions method reduces the splitting error from O(k2) to O(k3) in time step k. We prove convergence of this modified alternating directions procedure, for the usual non-mixed Galerkin finite element and finite difference cases, under the restriction that k/h2 is sufficiently small, where h is the grid spacing. This improve...

In this paper, we present new preconditioned generalized mixed-type splitting (GMTS) methods for solving weighted linear least square problems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GMTS methods converge faster than the GMTS method whenever the GMTS method is convergent. Finally...

| In this paper we fromulate and study a domain decomposition algorithm for solving mixed nite element approximations to parabolic initial-boundary value problems. In contrast to the usual overlapping domain decomposition method this technique leads to noniterative algorithms, i.e. the subdomain problems are solved independently and the solution in the whole domain is obtained from the local so...

We present an analysis of stationary solutions for two-dimensional (2D) Bose-Einstein condensates (BECs) with the Rashba spin-orbit (SO) coupling and Zeeman splitting. By introducing generalized momentum operator, linear version system can be solved exactly. The are semi-vortices Bessel-vortex (BV) modified (MBV) types, in presence weak strong splitting, respectively. ground states (GSs) full n...

We consider the numerical solution of elliptic boundary value problems by mixed nite element discretizations on simplicial triangulations. Emphasis is on the eecient iterative solution of the discretized problems by multilevel techniques and on adaptive grid reenement. The iterative process relies on a preconditioned conjugate gradient iteration in a suitably chosen subspace with a multilevel p...

We use the technique of updating the solution to suggest and analyze a class of new splitting methods for solving general mixed variational inequalities. It is shown that these modified methods converge for pseudomonotone operators, which is a weaker condition than monotonicity. Our methods differ from the known threestep forward-backward splitting of Glowinski, Le Tallec, and M. A. Noor for so...

In heavily populated areas, cell splitting used to increase the capacity of the cellular system. Cell splitting produces a cellular system with mixed cell sizes. Many previous studies assumed strength-based power control, which maintains received power at a desired level regardless of changes in the number of active users and in the amount of total other cells interference. However, with signal...

We study the well-posedness of initial value problems for scalar functional algebraic and differential functional equations of mixed type. We provide a practical way to determine whether such problems admit unique solutions that grow at a specified rate. In particular, we exploit the fact that the answer to such questions is encoded in an integer n. We show how this number can be tracked as a p...