Numerical methods for fuzzy differential inclusions
type: Item
instance of: scholarly article
title: Numerical methods for fuzzy differential inclusions
zbMATH Open document ID: 1074.65072
author: Tofigh Allahviranloo
author: Saeid Abbasbandy
author: Oscar Lopez-Pouso
author: Juan J. Nieto
publication date: 2005-06-01T00:00:00Z
review text: A numerical method for solving initial value problems for fuzzy differential inclusions is given. The fuzzy differential inclusions at each \(r\)-level, \(r\in [0,1]\), are given by \(x'(t) \in [f(t, x(t))]_r, x(0)\in [x_0]_r \) where the \(r\)-level set of \(u\) is \([u]_0= \text{supp}(u)\) and \( [u]_r = \{x\in\mathbb R^n; u(x)\geq r \}\) for \(r\in (0,1]\) and \( [f(\cdot, \cdot)]_r :[0,T] \times\mathbb R^n \to \kappa_c^n\) with \(\kappa_c^n\) the space of nonempty convex compact subsets of \(\mathbb R^n\). The paper is organized as follows: After introducing some basic results on fuzzy derivative and initial value problems, the authors propose a version of the two-stage Runge-Kutta method of Heun with order two for the above class of problems and prove the convergence of the approximate solution. Finally, the results of some numerical experiments are presented showing the \(r\)-level sets for a discrete set of values \( r \in [0,1]\), comparing with those obtained with explicit Euler's method.
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 26E50
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34A07
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 2173433
zbMATH Keywords: differential inclusions
zbMATH Keywords: fuzzy initial value problems
zbMATH Keywords: comparison of methods
zbMATH Keywords: Heun method
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
zbMATH Keywords: Euler's method
Wikidata QID: Q60199453
MaRDI profile type: Publication
full work available at URL: j.camwa.2004.03.009
OpenAlex ID: W2063047919
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DOI: 10.1016/J.CAMWA.2004.03.009
published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 2173433