Convergence of a semi-analytical method on the fuzzy linear systems

Document Type : Research Paper


1 Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

2 Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran


In this paper, we apply the  homotopy analysis method (HAM) for solving fuzzy  linear systems and present  the necessary and sufficient conditions for the convergence of series solution obtained via the HAM. Also, we present a new criterion for choosing a proper value of convergence-control parameter $\hbar$ when the HAM is applied to linear system of equations. Comparisons are made between the results of the HAM and several well-known numerical algorithms such as Jacobi method (JM), Gauss-Seidel method (GSM), successive over relaxation method (SOR), Adomian decomposition method (ADM) and homotopy perturbation method (HPM).


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