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

Authors

Mojtaba Ghanbari Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran

Rahele Nuraei Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract:

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

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 ...

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