Alternating Group Explicit Research Articles

The numerical solution of 2-dimensional fourth order partial differential equations by the age fractional method

The fourth order parabolic equation in two-space variables which arise in the study of transverse vibrations of a uniform plate is discussed and solved numerically using the Alternating Group Explicit (AGE) fractional method. The stability of the proposed scheme has been examined and shown to be uncondition-ally stable.

The iterative alternating decomposition explicit (iade) method to solve the heat conduction equation

Using the well-known fact of the parabolic-elliptic correspondence, a two-stage iterative explicit procedure of the Mitchell-Fairweather variant is developed to solve the one-dimensional parabolic problem. The method is shown to be more accurate than the recently developed Alternating Group Explicit (AGE) scheme. By the nature of its explicitness, the IADE method is suitable for application on parallel computers.

The parallel AGE method for the elliptic problem in two dimensions

In this paper the Alternating Group Explicit (AGE) method is presented for the iterative solution of the finite difference equations derived from the discretisation of an elliptic partial differential equation specified within a two-dimensional domain with given boundary conditions and implemented on a MIMD Balance system. The AGE method is shown to be eminently suitable for parallel computers since it possesses separate independent tasks i.e. (2×2) sub-blocks which can be expressed explicitly and can be executed simultaneously. Three parallel strategies are developed and implemented and the results compared.

The solution of nonlinear parabolic partial differential equations by the alternating group explicit (AGE) method

In this paper, nonlinear parabolic partial differential equations in one space dimension are solved numerically by using the alternating group explicit (AGE) method.

The numerical solution of the sine gordon partial differential equation by the age method

The Alternating Group Explicit (AGE) method is shown to be applicable for the iterative solution of the implicit difference equations of the sine Gordon nonlinear hyperbolic partial differential equation.

The solution of periodic parabolic equations by the coupled alternating group explicit (cage) iterative method

In this paper, parabolic differential equations with periodic boundary conditions in one space dimension (on a cylinder) are solved numerically by using the Alternating Group Explicit (AGE) iterative method [1]. It is shown that the two sweeps of the AGE algorithm can be combined into one, thus forming a stable explicit algorithm with reduced computational effort and suitable for implementation on a parallel computer.

The normalised alternating group explicit (nage) method

The alternating group explicit (AGE) method [1] has been applied to a variety of problems involving parabolic, hyperbolic and elliptic partial differential equations. The method has been shown to be extremely powerful and flexible and to be very suitable for use on vector and parallel computers. The practical implementation of it is considered here. The new scheme is shown to possess the same convergence property with a reduced computational effort.

The numerical solution of burgers' equation by the alternating group explicit (age) method

In this paper, nonlinear parabolic partial differential equations in one space dimension are solved numerically by using the Alternating Group Explicit (AGE) method (Evans, 1985).

The alternating group explicit (age) iterative method for solving parabolic equations II: 3 space dimensional problems

In Evans and Sahimi (1988), the Alternating Group Explicit (AGE) method was applied successfully to solve 2 space dimensional problems involving parabolic partial differential equations. Here the operator splitting technique used there is further extended to solve 3 dimensional parabolic problems.

The Solution of Two-Point Boundary Value Problems by the Alternating Group Explicit (AGE) Method

In this paper, a new explicit iterative solution for the finite difference equations of the two-point boundary value problem is given. In this new approach, the coefficient matrix of the obtained system is split into component matrices $G_1 $, $G_2 $, and an iterative method formulated which can be easily expressed in explicit form. Alternating this strategy on the grid points along the real axis results in the alternating group explicit (AGE) method analogous to the well-known ADI method.The convergence analysis of the new method is briefly discussed, its extension to multidimensional problems and the results of numerical experiments presented.

The alternating group explicit (age) iterative method for solving parabolic equations i: 2-dimensional problems

In Evans and Sahimi (1988), the Alternating Group Explicit (AGE) method was applied successfully to solve 2 space dimensional problems involving parabolic partial differential equations. Here the operator splitting technique used there is further extended to solve 3 dimensional parabolic problems.

The age Galerkin method for solving two-point boundary value problems

In this paper finite element Galerkin methods are developed for spaces of piecewise polynomial functions which are most suitable for two-point boundary value problems. The resulting banded linear systems are then solved by a block matrix iterative method which is an extension of the point alternating group explicit (AGE) method.

Alternating group explicit (AGE) iterative methods

In this paper the Alternating Group Explicit (AGE) methods, modified analogues of the classical Alternating Direction Implicit (ADI) methods, are introduced. Their explicit nature and their obvious parallelism, in contrast with the inherent parallelism of the ADI methods, makes them most suitable for the solution of the resulting linear systems arising from the discretisation of a class of elliptic PDEs on a Parallel Computer of SIMD (Single Instruction Stream-Multiple Data Stream) type. The determination of optimum sets of acceleration parameters in 2-dimensional problems is discussed and numerical experiments are successfully completed.

Group explicit iterative methods for solving large linear systems

In this paper, the Alternating Group Explicit (AGE) method is developed and applied to derive the solution of a 2 point boundary value problem. The analysis clearly shows the method to be analogous to the A.D.I. method. The extension of the method to ultidimensional problems and techniques for improving the convergence rate and attaining higher order accuracy are also given.

The Explicit Alternating Direction Methods ForPartial Differential Equations

In this paper, a method based on applying explicit algorithms for the solution of implicit finite difference systems approximating partial differential equations is introduced. The method arises from developing the concepts of the Alternating Group Explicit (AGE) methods introduced by Evans [2] and Evans and Sahimi in [6] and [7]. The new methods named The Explicit Alternating Direction (EAD) methods are introduced through applying them to the two dimensional heat conduction problem and the linear advection problem in two dimensions. A comparative study of the computational complexities of the AGE-2D and the EAD methods is also given.

The Numerical Solution of Parabolic and Elliptic Differential Equations

The Numerical Solution of Parabolic and Elliptic Differential Equations