Improved predictor-corrector method for solving fuzzy initial value problems
type: Item
instance of: scholarly article
title: Improved predictor-corrector method for solving fuzzy initial value problems
zbMATH Open document ID: 1165.65042
author: N. Ahmady
author: E. Ahmady
author: Tofigh Allahviranloo
author: Saeid Abbasbandy
published in: Information Sciences
publication date: 2009-03-24T00:00:00Z
review text: This paper is concerned with the numerical solution of initial value problems for first order fuzzy differential equations. First of all, after introducing some notations and definitions of fuzzy number, fuzzy set-valued mapping and (Hukuhara- and Seikkala-) differentiability, the Authors define the spline interpolation of a set of data \( \left( t_i, u_i \right)_{i=1}^n \) where \(t_i\) are real distinct numbers and \( u_i\) fuzzy numbers. Now, taking into account the integral equality \( y(t)= y(t_0) + \int_{t_0}^t y'(s) \, ds \) that holds for fuzzy set valued differentiable functions \( y(t)\) in both of the above senses, an explicit three step method based on interpolation of \(y'\)-values is derived and also similarly an implicit two step method. Further, a predictor corrector three step method based in the above methods is proposed. Standard stability and convergence proofs are provided. The paper ends with the numerical results of some elementary linear problems.
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 26E50
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 5531337
zbMATH Keywords: initial value problems
zbMATH Keywords: fuzzy differential equations
zbMATH Keywords: linear three step methods
zbMATH Keywords: predictor-corrector methods
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: numerical results
MaRDI profile type: Publication
full work available at URL: j.ins.2008.11.030
OpenAlex ID: W2050444457
cites work: Q4787290
cites work: Numerical methods for fuzzy differential inclusions
cites work: Tuning of reachable set in one dimensional fuzzy differential inclusions
cites work: Numerical solution of fuzzy differential equations by predictor-corrector method
cites work: Erratum to ``Numerical solution of fuzzy differential equations by predictor-corrector method'' [Inform. Sci. 177 (7) (2007) 1633-1647]
cites work: \(N\)th-order fuzzy linear differential equations
cites work: First order linear fuzzy differential equations under generalized differentiability
cites work: Note on ``Numerical solution of fuzzy differential equations by predictor-corrector method''
cites work: Revisiting fuzzy differential equations
cites work: On Fuzzy Mapping and Control
cites work: On fuzzy boundary value problems
cites work: Existence theorems to the Cauchy problem for fuzzy differential equations under compactness-type conditions
cites work: Brief note on the variation of constants formula for fuzzy differential equations
cites work: Towards fuzzy differential calculus. III: Differentiation
cites work: Q4490108
cites work: Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients
cites work: Numerical solutions of fuzzy differential and integral equations
cites work: On the validity of the Peano theorem for fuzzy differential equations
cites work: Initial value problems for higher-order fuzzy differential equations
cites work: Interpolation of fuzzy data
cites work: A note on fuzzy differential equations
cites work: Numerical solutions of fuzzy differential equations
cites work: Fuzzy differential equations and the extension principle
cites work: The Cauchy problem for continuous fuzzy differential equations
cites work: Bounded solutions for fuzzy differential and integral equations
cites work: LINEAR FIRST-ORDER FUZZY DIFFERENTIAL EQUATIONS
cites work: Q3527104
cites work: Initial and boundary value problems for fuzzy differential equations.
cites work: Comparison results for fuzzy differential equations
cites work: Monotone method for fuzzy differential equations
cites work: Embedding of level-continuous fuzzy sets on Banach spaces
cites work: On the fuzzy initial value problem
cites work: Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations
cites work: A class of linear differential dynamical systems with fuzzy initial condition
cites work: On the structure of solutions for fuzzy initial value problem
DOI: 10.1016/J.INS.2008.11.030
description: scientific article; zbMATH DE number 5531337