In this study, iterative methods particularly families of Alternating Group Explicit (AGE) methods are used to solve system of linear equations generated from the discretization of two-point fuzzy boundary value problems (FBVPs) The formulation and implementation of the Full-Sweep AGE (FSAGE) and Half-Sweep AGE (HSAGE) methods were also presented Then numerical experiments are carried out onto two example problems to verify the effectiveness of the methods

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Performance of HSAGE method with seikkala derivative for 2-D fuzzy poisson equation

A modified backward difference time discretization is presented for Galerkin approximations for nonlinear hyperbolic equation in two space variables. This procedure uses a local approximation of the coefficients based on patches of finite elements with these procedures, a multidimensional problem can be solved as a series of one-dimensional problems. Optimal order H01 and L2 error estimates are derived. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007

A new alternating-direction finite element method for hyperbolic equation

In this article, a new weight tri-diagonal iterative method in solving system of linear equation is proposed and its convergence is discussed. The set of methods in solving linear system generated by high-order scheme for solving one-dimensional Poisson equation and one-dimensional heat equation with periodic boundary are presented. The numerical experiments shows that the proposed method demonstrates a better performance compared with weight Jacobi, successive-over relaxation and alternating group explicit methods.

On a new weight tri-diagonal iterative method and its applications

The aim of this paper deals with the performance of Alternating Group Explicit (AGE) iterative method for solving the linear system based on Caputo’s finite difference approximation equation. Actually, the approximation equation was be generated from the discretization process of the fractional two-point boundary value problems by using finite difference discretization scheme and Caputo’s operator. The formulation and implementation of AGE iterative method have been included. To investigate the efficiency of AGE iterative method, this paper considered four examples of numerical experiments. Based on numerical results, the findings showed that the AGE method is more efficient as compared with GS method.

Caputo’s Finite Difference Solution of Fractional Two-Point BVPs Using AGE Iteration

We report a new three-point compact sixth-order approximation for the solution of nonlinear two-point boundary value problems $$ {-}w^{\prime\prime} + f\left( {t,w} \right) = 0 $$, subject to natural boundary conditions prescribed at two end points. We also discuss the application of single-step alternating group explicit (SAGE) iteration method to the nonlinear difference equation as a computational tool. The error analysis of the SAGE iteration method is discussed briefly. We have compared the results obtained by using the proposed SAGE iteration method with the results obtained by corresponding two-step alternating group explicit iteration method to demonstrate experimentally the superiority of the proposed method.

A new sixth-order approximation for nonlinear two-point boundary value problems: application of single-step alternating group explicit iteration method to engineering problems

In this paper, the recently introduced Alternating Group Explicit (AGE) method is compared with the well-known Successive Overrelaxation (SOR) methods. Both theoretical and experimental results confirm that the two methods have similar convergence rates.

Comparison of SOR and AGE methods for solution of the two-point boundary value problem

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 (in Int. J. Comput. Math., 1985, 17, 81–108) and Evans & Sahimi (Int. J. Comput. Math., 1988, 24, 311–341; 1991, 41, 115–122). 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. Finally an illustration of how the EAD method may be applied to a fluid mechanics problem such as the shallow water equations is also given.

The Explicit Alternating Direction methods and their applications to problems in fluid mechanics

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Comparison of SOR and AGE methods for solution of the two-point boundary value problem

The Explicit Alternating Direction methods and their applications to problems in fluid mechanics