Numerical solutions of fuzzy differential equations
type: Item
instance of: scholarly article
title: Numerical solutions of fuzzy differential equations
zbMATH Open document ID: 0939.65086
DOI: 10.1016/S0165-0114(97)00233-9
author: Ming Ma
author: Menahem Friedman
author: A. Kandel
published in: Fuzzy Sets and Systems
publication date: 2000-06-19T00:00:00Z
review text: The authors study the explicit Euler approximation of a Cauchy problem for fuzzy (ordinary) differential equations. By the embedding approach, the original problem in a Banach space with supremum norm is replaced by two parametric, first-order ordinary differential equations. These differential equations can be solved by classical numerical algorithms. The authors present a pointwise convergence theorem for the standard Euler method in the given Banach space under uniform boundedness of second derivatives, Lipschitz-continuous right hand sides and for equidistant stepsize selection. 5 examples (both linear and nonlinear) are exhibited and discussed in view of the implementation of the explicit Euler approximation. A standard, two-dimensional error estimation is given in terms of the global Lipschitz constant, the length of integration interval \(T-t_0\), and the equidistant stepsize \(h\).
reviewed by: Henri Schurz
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 65J10
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 1339611
zbMATH Keywords: fuzzy differential equations
zbMATH Keywords: fuzzy numbers
zbMATH Keywords: Euler method
zbMATH Keywords: fuzzy Cauchy problem
zbMATH Keywords: fuzzy dynamical systems
zbMATH Keywords: Banach space
zbMATH Keywords: convergence
zbMATH Keywords: stepsize selection
zbMATH Keywords: linear
zbMATH Keywords: nonlinear
zbMATH Keywords: error estimation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1339611