Numerical solution of fuzzy differential equations under generalized differentiability

In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. Then we show that any suitable numerical method for...

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Bibliographic Details
Published in:Nonlinear analysis. Hybrid systems 2009-11, Vol.3 (4), p.700-707
Main Authors: Nieto, J.J., Khastan, A., Ivaz, K.
Format: Article
Language:English
Subjects:
Fuzzy differential equations
Generalized Characterization Theorem
Generalized differentiability
Generalized Euler method
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Summary:In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized Characterization Theorem, we investigate the problem of finding a numerical approximation of solutions. Then we show that any suitable numerical method for ODEs can be applied to solve numerically fuzzy differential equations under generalized differentiability. The generalized Euler approximation method is implemented and its error analysis, which guarantees pointwise convergence, is given. The method’s applicability is illustrated by solving a linear first-order fuzzy differential equation.
ISSN:1751-570X
DOI:10.1016/j.nahs.2009.06.013