Numerical solution of hybrid fuzzy differential equations by predictor-corrector method

Prakash, P.; Kalaiselvi, V.K.G.

doi:10.1080/00207160802247620

Cited by 18 publications

(5 citation statements)

References 8 publications

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“…Tese dynamic behaviors with Zadeh's fuzzy theory [1] paved a way to fuzzy diferential equations [2][3][4][5] and fuzzy hybrid diferential equations (FHDEs) [5][6][7][8][9][10][11][12][13][14][15]. In the present paper, two sixth-order methods called RK-Huta and RK-Butcher, respectively, having eight stages and seven stages are used to obtain approximate solutions of FHDE.…”

Section: Introductionmentioning

confidence: 99%

“…Other than them, Salahshour along with Allahviranloo and Ahmadian et al made remarkable contributions in hybrid fuzzy diferential equations [20,21]. Te readers are encouraged to go through the various applications of numerical methods to solve various types of diferential equations through [4][5][6][7][8][9][10][11][12][13][14][15][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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On New Solutions of Fuzzy Hybrid Differential Equations by Novel Approaches

Dhandapani,

Thippan,

Unyong

et al. 2023

Journal of Mathematics

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The goal of this paper is to find the best of two sixth-order methods, namely, RK-Huta and RK–Butcher methods for solving the fuzzy hybrid systems. We state a necessary definition and theorem in terms of consistency for convergence, and finally, we compare the obtained numerical results of two different methods with analytical solution using two different numerical examples. In addition to that, we generalize the solutions obtained by RK-6 Huta and RK-6 Butcher methods (same order different stage methods) for both the problems we handled. We are proposing these two methods in order to reduce the error in accuracy and to establish these two methods are better than any other existing numerical methods. The best of two sixth-order methods are found by the error analysis study for both the problems. Also, we show whether the change in number of stages of same order methods affects the accuracy of the approximation or not.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On New Solutions of Fuzzy Hybrid Differential Equations by Novel Approaches

Dhandapani,

Thippan,

Unyong

et al. 2023

Journal of Mathematics

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“…Fuzzy Differential Equation (FDE) models have wide range of applications in many branches of engineering and in the field of medicine. The concept of a fuzzy derivative was first introduced by Chang and Zadeh [5], later Dubois and Prade [6] defined the fuzzy derivative by using Zadeh"s extension principle and then followed by Puri and Ralescu [23]. Fuzzy differential equations have been suggested as a way of modelling uncertain and incompletely specified systems and were studied by many researchers [9,10].…”

Section: Introductionmentioning

confidence: 99%

Fourth Order Runge-Kutta Method Based On Geometric Mean for Hybrid Fuzzy Initial Value Problems

Sharmila¹

2017

IOSR JM

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“…Indeed, the generalized derivative is defined for a larger class of fuzzy-number-valued functions than the Hukuhara derivative. Some applications of numerical methods in FDE and hybrid fuzzy differential equation (HFDE) are presented in [9][10][11][12][13][14][15][16][17][18][19]. Some other approaches to study FDE and fuzzy dynamical systems have been investigated in [20][21][22].…”

Section: Introductionmentioning

confidence: 99%