Bede, Barnabás Note on “Numerical solution of fuzzy differential equations by predictor-corrector method”. (Note on “Numerical solutions of fuzzy differential equations by predictor-corrector method”.) (English) Zbl 1183.65092 Inf. Sci. 178, No. 7, 1917-1922 (2008). Summary: In the present note it is shown that the examples presented in a recent paper by T. Allahviranloo et al. [Inf. Sci. 177, No. 7, 1633–1647 (2007; Zbl 1183.65090)], are incorrect. Namely, the “exact solutions” proposed by the authors are not solutions of the given fuzzy differential equations (FDEs). The correct exact solutions are also presented here, together with some results for characterizing solutions of FDEs under Hukuhara differentiability by an equivalent system of ODEs. In this way a new direction for the numerical solutions of FDEs is proposed. Cited in 3 ReviewsCited in 53 Documents MSC: 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations Keywords:fuzzy numbers; fuzzy differential equations; Hukuhara differentiability Citations:Zbl 1183.65090 PDFBibTeX XMLCite \textit{B. Bede}, Inf. Sci. 178, No. 7, 1917--1922 (2008; Zbl 1183.65092) Full Text: DOI References: [1] Allahviranloo, T.; Ahmady, N.; Ahmady, E., Numerical solution of fuzzy differential equations by predictor-corrector method, Information Sciences, 177, 1633-1647 (2007) · Zbl 1183.65090 [2] Allahviranloo, T.; Ahmady, N.; Ahmady, E., Two step method for fuzzy differential equations, International Mathematical Forum, 1, 823-832 (2006) · Zbl 1143.65357 [3] Bede, B.; Gnana Bhaskar, T.; Lakshmikantham, V., Perspectives of fuzzy initial value problems, Communications in Applied Analysis, 11, 339-358 (2007) · Zbl 1152.34041 [4] Y. Chalco-Cano, H. Román-Flores, On new solutions of fuzzy differential equations, Chaos, Solitons and Fractals (2006), doi:10.1016/j.chaos.2006.10.043.; Y. Chalco-Cano, H. Román-Flores, On new solutions of fuzzy differential equations, Chaos, Solitons and Fractals (2006), doi:10.1016/j.chaos.2006.10.043. [5] Ding, Z.; Ma, M.; Kandel, A., Existence of the solutions of fuzzy differential equations with parameters, Information Sciences, 99, 205-217 (1997) · Zbl 0914.34057 [6] Kaleva, O., Fuzzy differential equations, Fuzzy Sets and Systems, 24, 301-317 (1987) · Zbl 0646.34019 [7] Kaleva, O., A note on fuzzy differential equations, Nonlinear Analysis, 64, 895-900 (2006) · Zbl 1100.34500 [8] Puri, M.; Ralescu, D., Differentials of fuzzy functions, Journal of Mathematical Analysis and Applications, 91, 552-558 (1983) · Zbl 0528.54009 [9] Seikkala, S., On the fuzzy initial value problem, Fuzzy Sets and Systems, 24, 319-330 (1987) · Zbl 0643.34005 [10] Song, S.; Wu, C., Existence and uniqueness of solutions to the Cauchy problem of fuzzy differential equations, Fuzzy Sets and Systems, 110, 55-67 (2000) · Zbl 0946.34054 [11] L. Stefanini, On the generalized LU-fuzzy derivative and fuzzy differential equations, in: IEEE International Fuzzy Systems Conference, FUZZ-IEEE, London, UK, 23-26 July 2007, pp. 1-6.; L. Stefanini, On the generalized LU-fuzzy derivative and fuzzy differential equations, in: IEEE International Fuzzy Systems Conference, FUZZ-IEEE, London, UK, 23-26 July 2007, pp. 1-6. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.