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Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem. (English) Zbl 1165.65041

Hybrid fuzzy differential initial value problems are systems that evolve in continuous time like differential systems but undergo fundamental changes in their governing fuzzy equations at a sequence of discrete times. In a previous paper [Nonlinear Anal., Hybrid Syst. 2, No. 2, 626–634 (2008; Zbl 1155.93370)] the authors of this paper have studied some Runge-Kutta type methods for the numerical solution of these equations.

Now they follow an alternative approach by using a recent characterization theorem due to B. Bede [Inf. Sci. 178, No. 7, 1917–1922 (2008; Zbl 1183.65092)] for fuzzy differential equations that, under suitable conditions, permits to solve initial value problems for these equations converting them in systems of ordinary differential equations. The main result of the present paper is an extension of Bede’s characterization theorem for hybrid fuzzy IVPs so that any stable one step numerical method for ODEs can be applied piecewise to solve numerically IVPs for hybrid fuzzy differential equations.

MSC:
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
26E50Fuzzy real analysis
65L06Multistep, Runge-Kutta, and extrapolation methods
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