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

Ghanbari, Mojtaba; Nuraei, Rahele

doi:10.22111/ijfs.2014.1623

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	Convergence of a semi-analytical method on the fuzzy linear systems
Iranian Journal of Fuzzy Systems
مقاله 5، دوره 11، شماره 4، آبان 2014، صفحه 45-60 اصل مقاله (414.87 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1623
نویسندگان
Mojtaba Ghanbari^* ¹؛ Rahele Nuraei²
¹Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran
²Department of Mathematics, South Tehran Branch, Islamic Azad University, Tehran, Iran
چکیده
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).
کلیدواژه‌ها
Fuzzy linear system؛ Homotopy analysis method؛ Convergence-control parameter؛ Numerical algorithms

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