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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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 |
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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 |
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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. |
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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 |
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2018 |
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http://eprints.um.edu.my/22630/ https://doi.org/10.1016/j.fss.2016.11.013 |
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1648736164991991808 |
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13.18916 |