Solution of lyapunov equations by alternating direction implicit iteration

Modified alternating direction-implicit iteration method for linear systems from the incompressible Navier-Stokes equations

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An Alternating Direction Implicit Method for Modeling of Fluid Flow

This research includes of the numerical modeling of fluids in two-dimensional cavity. The cavity flow is an important theoretical problem. In this research, modeling was carried out based on an alternating direction implicit via Vorticity-Stream function formulation. It evaluates different Reynolds numbers and grid sizes. Therefore, for the flow field analysis and prove of the ability of the sc...

Implicit Alternating Direction Methods

in general plane regions and with respect to linear boundary conditions, is a classical problem of numerical analysis. Many such boundary value problems have been solved successfully on high-speed computing machines, using the (iterative) Young-Frankel "successive overrelaxation" (SOR) method as defined in [l] and [2], and variants thereof ("line" and "block" overrelaxation). For this method, e...

On Accuracy of Alternating Direction Implicit Methods for Parabolic Equations

We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematical description. However, we often observe i...

Solving Two-Dimensional Fuzzy Partial Dierential Equation by the Alternating Direction Implicit Method