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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.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
46S40 Fuzzy functional analysis
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
26E50 Fuzzy real analysis
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References:

[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), Taylor and Francis: Taylor and Francis United Kingdom · 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.; Allah Viranloo, T., Numerical solution of fuzzy differential equations by Taylor method, J. Comput. Methods Appl. Math., 2, 113-124 (2002) · Zbl 1019.34061
[6] Abbasbandy, S.; Allah Viranloo, T., Numerical solution of fuzzy differential equation, Math. Comput. Appl., 7, 41-52 (2002) · Zbl 1013.65070
[7] Abbasbandy, S.; Allah Viranloo, T., 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
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.