Extended Simpson Rule for Solving First-Order Fuzzy Differential Equations Using Generalized Differentiability

Reza Afsharinafar (), Fudziah Ismail (), Mohamed Suleiman () and Ali Ahmadian Hosseini ()
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Reza Afsharinafar: Universiti Putra Malaysia, Institute for Mathematical Research
Fudziah Ismail: Universiti Putra Malaysia, Mathematics Department, Science Faculty
Mohamed Suleiman: Universiti Putra Malaysia
Ali Ahmadian Hosseini: Universiti Putra Malaysia

A chapter in International Conference on Mathematical Sciences and Statistics 2013, 2014, pp 91-101 from Springer

Abstract: Abstract In this present paper, extended Milne–Simpson rule is applied to find the fuzzy solutions of first order fuzzy differential equations (FDEs) under generalized Hukuhara differentiability concept. Based on the work done by Chalco-Cano we show how FDEs can be transformed to a system of ordinary differential equations. Then to find the solutions of fuzzy initial value problems (FIVPs), the Milne–Simpson formula is generalized. The errors, which guarantee pointwise convergence, are compared with other established methods which clearly show the advantage of our method for solving FIVPs.

Keywords: Order Fuzzy Differential Equation; Generalized Differentiability; Fuzzy Initial Value Problem (FIVP); Fuzzy Solution; Hukuhara Derivative (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-4585-33-0_10

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DOI: 10.1007/978-981-4585-33-0_10

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