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: | , , , |
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Format: | Article |
Published: |
Elsevier
2018
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Subjects: | |
Online Access: | http://eprints.um.edu.my/22630/ https://doi.org/10.1016/j.fss.2016.11.013 |
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Summary: | 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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