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Numerical solution to hybrid fuzzy systems. (English) Zbl 1123.65069
The well known Euler method for the numerical solution of ordinary differential equations is extended to fuzzy differential equations. A brief convergence analysis is given.

65L05Initial value problems for ODE (numerical methods)
46S40Fuzzy functional analysis
65L06Multistep, Runge-Kutta, and extrapolation methods
34A34Nonlinear ODE and systems, general
26E50Fuzzy real analysis
Full Text: DOI
[1] Lakshmikantham, V.; Liu, X. Z.: Impulsive hybrid systems and stability theory. Internat. J. Nonlinear differential equations 5, 9-17 (1999) · Zbl 0901.34018
[2] Lakshmikantham, V.; Mohapatra, R. N.: Theory of fuzzy differential equations and inclusions. (2003) · Zbl 1072.34001
[3] Sambandham, M.: Perturbed Lyapunov-like functions and hybrid fuzzy differential equations. Internat. J. Hybrid syst. 2, 23-34 (2002)
[4] Ma, M.; Friedman, M.; Kandel, A.: Numerical solutions of fuzzy differential equations. Fuzzy sets and systems 105, 133-138 (1999) · Zbl 0939.65086
[5] Abbasbandy, S.; Viranloo, T. Allah: Numerical solution of fuzzy differential equations by Taylor method. J. comput. Methods appl. Math. 2, 113-124 (2002) · Zbl 1019.34061
[6] Abbasbandy, S.; Viranloo, T. Allah: Numerical solution of fuzzy differential equation. Math. comput. Appl. 7, 41-52 (2002) · Zbl 1013.65070
[7] Abbasbandy, S.; Viranloo, T. Allah: Numerical solution of fuzzy differential equation by Runge--Kutta method. Nonlinear stud. 11, 117-129 (2004) · Zbl 1056.65069
[8] Kaleva, O.: Fuzzy differential equations. Fuzzy sets and systems 24, 301-317 (1987) · Zbl 0646.34019
[9] Goetschel, R.; Voxman, W.: Elementary fuzzy calculus. Fuzzy sets and systems 18, 31-43 (1986) · Zbl 0626.26014
[10] Wu, C. -X.; Ma, M.: Embedding problem of fuzzy number space: part I. Fuzzy sets and systems 44, 33-38 (1991) · Zbl 0757.46066