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The Adomian decomposition method for fuzzy system of linear equations. (English) Zbl 1069.65025

Summary: The application of the Adomian method for solving fuzzy system of linear equations (FSLE) is considered. For an FSLE the author has shown that the Adomian decomposition method is equivalent to the Jacobi iterative method [Appl. Math. Comput. 155, No. 2, 493–502 (2004; Zbl 1067.65040)]. The algorithm is illustrated by solving some numerical examples.

MSC:

65F10 Iterative numerical methods for linear systems
08A72 Fuzzy algebraic structures

Citations:

Zbl 1067.65040
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Full Text: DOI

References:

[1] Friedman, M.; Ming, M.; Kandel, A., Fuzzy linear systems, FSS, 96, 201-209 (1998) · Zbl 0929.15004
[2] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Appl. Math. Comput., in press; T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Appl. Math. Comput., in press · Zbl 1067.65040
[3] Adomian, G., Nonlinear Stochastic Systems Theory and Applications to Physics (1989), Kluwer: Kluwer Dordrecht, Holland · Zbl 0659.93003
[4] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer · Zbl 0802.65122
[5] Abbaoui, K.; Cherruault, Y., Convergence of Adomian’s method applied to differential equations, Math. Comput. Modeling, 28, 5, 103-110 (1994) · Zbl 0809.65073
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