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Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability

In this paper, an extended fourth-order Runge–Kutta method is studied to approximate the solutions of first-order fuzzy differential equations using a generalized characterization theorem. In this method, new parameters are utilized in order to enhance the order of accuracy of the solutions using ev...

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Main Authors: Ahmadian, Ali, Salahshour, Soheil, Chan, Chee Seng, Baleanu, Dumitru
Format: Article
Published: Elsevier 2018
Subjects:
QA Mathematics
QA75 Electronic computers. Computer science
Online Access:http://eprints.um.edu.my/22630/
https://doi.org/10.1016/j.fss.2016.11.013
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spelling my.um.eprints.226302019-09-30T08:29:06Z http://eprints.um.edu.my/22630/ Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability Ahmadian, Ali Salahshour, Soheil Chan, Chee Seng Baleanu, Dumitru QA Mathematics QA75 Electronic computers. Computer science In this paper, an extended fourth-order Runge–Kutta method is studied to approximate the solutions of first-order fuzzy differential equations using a generalized characterization theorem. In this method, new parameters are utilized in order to enhance the order of accuracy of the solutions using evaluations of both f and f′, instead of using the evaluations of f only. The proposed extended Runge–Kutta method and its error analysis, which guarantees pointwise convergence, are given in detail. Furthermore, the accuracy and efficiency of the proposed method are demonstrated in a series of numerical experiments. Elsevier 2018 Article PeerReviewed Ahmadian, Ali and Salahshour, Soheil and Chan, Chee Seng and Baleanu, Dumitru (2018) Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability. Fuzzy Sets and Systems, 331. pp. 47-67. ISSN 0165-0114 https://doi.org/10.1016/j.fss.2016.11.013 doi:10.1016/j.fss.2016.11.013
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
QA75 Electronic computers. Computer science
spellingShingle QA Mathematics
QA75 Electronic computers. Computer science
Ahmadian, Ali
Salahshour, Soheil
Chan, Chee Seng
Baleanu, Dumitru
Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability
description In this paper, an extended fourth-order Runge–Kutta method is studied to approximate the solutions of first-order fuzzy differential equations using a generalized characterization theorem. In this method, new parameters are utilized in order to enhance the order of accuracy of the solutions using evaluations of both f and f′, instead of using the evaluations of f only. The proposed extended Runge–Kutta method and its error analysis, which guarantees pointwise convergence, are given in detail. Furthermore, the accuracy and efficiency of the proposed method are demonstrated in a series of numerical experiments.
format Article
author Ahmadian, Ali
Salahshour, Soheil
Chan, Chee Seng
Baleanu, Dumitru
author_facet Ahmadian, Ali
Salahshour, Soheil
Chan, Chee Seng
Baleanu, Dumitru
author_sort Ahmadian, Ali
title Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability
title_short Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability
title_full Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability
title_fullStr Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability
title_full_unstemmed Numerical solutions of fuzzy differential equations by an efficient Runge–Kutta method with generalized differentiability
title_sort numerical solutions of fuzzy differential equations by an efficient runge–kutta method with generalized differentiability
publisher Elsevier
publishDate 2018
url http://eprints.um.edu.my/22630/
https://doi.org/10.1016/j.fss.2016.11.013
_version_ 1648736164991991808
score 13.18916

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