Generalized Hukuhara Differentiability of Interval-valued Functions and Interval Differential Equations

Luciano Stefanini () and Barnabas Bede ()
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Barnabas Bede: Department of Mathematics, University of Texas-Pan American, Edimburg, Texas (USA)

No 803, Working Papers from University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini

Abstract: In the present paper we introduce and study a generalization of the Hukuhara differ- ence and also generalizations of the Hukuhara differentiability to the case of interval valued functions. We consider several possible definitions for the derivative of an interval valued function and we study connections between them and their proper- ties. Using these concepts we study interval differential equations. Local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ODE systems and by differential algebraic equations. We also show some connection with differential inclusions. The thoretical results are turned into practical algorithms to solve interval differential equations.

Keywords: Interval Arithmetic; Interval Differentiability; Hukuhara Difference; Hukuhara Derivative; Interval Differential Equations. (search for similar items in EconPapers)
JEL-codes: C00 C60 C63 C88 D80 (search for similar items in EconPapers)
Pages: 39 pages
Date: 2008, Revised 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (11)

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