Numerical solutions of two-point fuzzy boundary value problem using half-sweep alternating group explicit method

Abstract

Articles you may be interested inNumerical solutions for linear Fredholm integral equations of the second kind using 2-point half-sweep explicit group method AIP Conf. ABCs and fourth-order spline collocation for the solution of two-point boundary value problems over an infinite domain AIP Conf. Proc. 1558, 372 (2013); 10.1063/1.4825501 Quarter-sweep Gauss-Seidel method with quadratic spline scheme applied to fourth order two-point boundary value problems AIP Conf. Proc. 1522, 735 (2013); 10.1063/1.4801199Successive over relaxation method in solving two-point fuzzy boundary value problems AIP Conf.Abstract. The main purpose of this paper is to examine the application of complexity reduction approach based on halfsweep iteration concept with Alternating Group Explicit (AGE) method namely Half-Sweep AGE (HSAGE) method for solving system of linear equations generated from the discretization of two-point fuzzy boundary value problems (FBVPs). To form the linear system, the corresponding second order finite difference scheme has been used to derive the half-sweep finite difference approximation equation of the problems. The formulation and implementation of the proposed iterative method are discussed. Furthermore, numerical results of two test problems are also included in order to verify performance of the method compared to Full-Sweep Gauss-Seidel (FSGS) and Full-Sweep AGE (FSAGE) methods. The findings show that the proposed HSAGE method is superior to other tested methods in the sense of number of iterations, execution time and Hausdorff distance.

Redlich-Kister Finite Difference Solution for Solving Two-Point Boundary Value Problems by using Ksor Iteration Family

“…Therefore, the combination of the KSOR block technique with the standard EG iterative method can reduce iteration and Time compared to the KSOR point approach. For further study, this paper can be extended to perform the use of the newly established RKFD discretization scheme for solving the multi-dimensional boundary value problems by using the twostep iteration family [43,44], and the half-sweep [45,46] and quarter-sweep [47,48] iteration families.…”

Implementation of TAGE Method Using Seikkala Derivatives Applied to Two-Point Fuzzy Boundary Value Problems

“…Basically the results of this paper can be classified as one of full-sweep iteration. Apart from the concept of the full-sweep iteration, further investigation of half-sweep [19][20][21][22][23][24] and quarter-sweep [25][26][27] iterations can also be considered in order to speed up the convergence rate of the standard proposed iterative methods.…”

Numerical solution of fuzzy boundary value problems using Galerkin method

“…The above system (14) can be written in the form of a linear system of equations AX ¼ B as follows: We may write Eqs. (19) and 20as the following system is obtained:…”

“…Undetermined fuzzy coefficients method has been applied by Guo et al [18] to obtain the solution of SOFBVPs. Dahalan et al [19] implemented half-sweep alternating group explicit method to obtain the numerical solution. Optimal homotopy asymptotic method (OHAM) has been applied by Jameel and Ismail [20] to solve nth order two-point FBVPs.…”