Application of Homotopy Perturbation Method for Fuzzy Linear Systems and Comparison with Adomian’s Decomposition Method

Abstract

We present an efficient numerical algorithm for solution of the fuzzy linear systems (FLS) based on He’s homotopy perturbation method (HPM). Moreover, the convergence properties of the proposed method have been analyzed and also comparisons are made between Adomian’s decomposition method (ADM) and the proposed method. The results reveal that our method is effective and simple.

LU Decomposition Scheme for Solving m-Polar Fuzzy System of Linear Equations

“…Allahviranloo et al [27][28][29][30] developed some important numerical schemes for solving a fuzzy linear system of equations (FLSEs). Moreover, certain methods to solve fuzzy linear systems have been discussed in [31][32][33][34]. Akram et al [35][36][37][38][39] studied certain schemes for solving the bipolar fuzzy linear system of equations.…”

On the Application of Homotopy Perturbation Method for Solving Systems of Linear Equations

“…Liu [ 13 ] by using HPM and splitting methods proposed a new method for linear systems. Saberi Najafi et al [ 14 ] based on HPM proposed a new algorithm for fuzzy linear systems and compared it with Adomian's decomposition method. They also in [ 15 ] show that solving linear systems by using a new method called modified HPM, presented by Noor et al [ 16 ], is impractical.…”

The Mixed Type Splitting Methods for Solving Fuzzy Linear Systems

“…In [1,2] Kandel et al applied the embedding method for fuzzy linear system (hereafter denoted by FLS) and replaced the FLS by a 2 × 2 crisp linear system. This model has been modified later by some other researchers; see [10][11][12][13][14][15][16] and the references therein.…”