Adomian Method for Second-order Fuzzy Differential Equation
In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331901Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2169
 S. Abbasbandy, T. Allahviranloo, Numerical solutions of fuzzy differential equations by Taylor method, Journal of Computer and Mathematics with Applications 2 (2002) 113-124
 S. Abbasbandy, T. Allahviranloo, O. Lopez-Pouso, J.J. Nieto, Numerical methods for fuzzy differential inclusions, Journal of Computer and Mathematics with Applications 48 (2004) 1633-1641.
 G. Adomian, Nonlinear stochastic systems and application to physics, Kluwer, Dordecht,1989.
 G. Adomian, A review of the decomposition method and some results for nonlinear equations, Math. Compute Model 7 (1990) 17-43.
 G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer,Dordecht, 1994.
 T. Allahviranloo, N. Ahmadi, E. Ahmadi, Numerical solution of fuzzy differential equations by predictor-corrector method, Information Sciences 177 (2007) 1633-1647.
 E. Babolian , H. Sadeghi b, Sh. Javadi. Numerically solution of fuzzy differential equations by Adomian method, Applied Mathematics and Computation 149 (2004) 547-557.
 B. Bede, S.G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Sets and Systems 147 (2004) 385-403.
 B. Bede, S.G. Gal, Generalizations of the differentiability of fuzzy number value functions with applications to fuzzy differential equations, Fuzzy Sets and Systems 151 (2005) 581-599.
 B. Bede, I.J. Rudas, A.L. Bencsik, First order linear fuzzy differential equations under generalized differentiability, Information Sciences 177 (2007)1648-1662.
 J.J. Buckley, T. Feuring, Fuzzy differential equations, Fuzzy Sets and Systems 110 (2000) 43-54.
 Y. Chalco-Cano, H. Romn-Flores, Comparison between some approaches to solve fuzzy differential equations, Fuzzy Sets and Systems 160 (2009)1517-1527.
 S. L. Chang, L. A. Zadeh, On fuzzy mapping and control, IEEE Transactions on Systems Man Cybernetics 2 (1972) 330-340.
 D. Dubois, H. Prade, Towards fuzzy differential calculus: Part 3, Differentiation. Fuzzy Sets and Systems 8 (1982) 225-233.
 D. Dubois, H. Prade, Fuzzy numbers: an overview, in: J. Bezdek (Ed.), Analysis of Fuzzy Information, CRC Press (1987) 112-148.
 M. Friedman, M. Ma, A. Kandel, Numerical solution of fuzzy differential and integral equations, Fuzzy Sets and Systems 106 (1999) 35-48.
 S. G. Gal, Approximation theory in fuzzy setting, in: G.A. Anastassiou (Ed.), Handbook of Analytic-Computational Methods in Applied Mathematics, Chapman Hall/CRC Press, (2000) 617-666.
 E. Hllermeier, An approach to modelling and simulation of uncertain systems, International Journal of Uncertainty Fuzziness Knowledge-Based Systems 5 (1997) 117-137.
 E. Hllermeier, Numerical methods for fuzzy initial value problems, International Journal of Uncertainty Fuzziness Knowledge-Based Systems 7 (1999) 439-461.
 O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987) 301-317.
 A. Kandel, W. J. Byatt, Fuzzy differential equations, in: Proceedings of International Conference Cybernetics and Society, Tokyo: (1978) 1213- 1216.
 A. Kandel, W. J. Byatt, Fuzzy processes, Fuzzy Sets and Systems 4 (1980 )117-152.
 A. Khastan, F. Bahrami, K. Ivaz, New results on multiple solutions for nth-order fuzzy differential equation under generalized differentiability. Boundary Value Problem (Hindawi Publishing Corporation). doi:10.1155/2009/395714 (2010).
 A. Khastan, K. Ivaz, Numerical solution of fuzzy differential equations by Nystr?m method. Chaos Solitons Fractals 41 (2009) 859-868.
 J.J. Nieto, R. Rodr┼éguez-Lpez, D. Franco, Linear first-order fuzzy differential equation, International Journal of Uncertainty Fuzziness Knowledge-Based Systems 14 (2006) 687-709.
 M. Puri, D. Ralescu. Differentials of fuzzy functions.Journal of Mathematical Analysis and Applications 91(1983) 552-558.
 S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems 24 (1987) 319-330.
 S. J .Song, C. X. Wu, Existence and uniqueness of solutions to the Cauchy problem of fuzzy differential equations, Fuzzy Sets and Systems 110 (2000) 55-67.
 J. P. Xu, Z. Liao, Z. Hu, A class of linear differential dynamical systems with fuzzy initial condition. Fuzzy Sets and Systems 158 (2007) 2339- 2358.