F^1-transform of Functions of Two Variables

Hoďáková, Petra; Perfilieva, Irina

doi:10.2991/eusflat.2013.83

Cited by 8 publications

(2 citation statements)

References 6 publications

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“…, Y n ] of the FzT for the functions x(t) and y(t). The problem with the previous scheme (22) is that the unknown quantities F k+1 and G k+1 which means that X k+1 (Y k+1 ) appears on both sides and an implicit method. Therefore, one solution to this problem would be to use an explicit method such as another fuzzy approach, namely Scheme I.…”

Section: Numerical Scheme I: Modified Trapezoidal Rule Based On Fzt Amentioning

confidence: 99%

“…FzT of two variables based on finite differences method was used by [21] for solving a type of partial differential equations with Dirichlet boundary conditions and initial conditions. In addition, the first degree FzT of two variables was introduced by [22]. By [23], the partial derivatives using the first FzT were approximated and modification of the Canny edge detector was proposed.…”

Section: Introductionmentioning

confidence: 99%

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New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II

ALKasasbeh

Perfilieva

Ahmad

et al. 2018

ASI

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In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.

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Section: Numerical Scheme I: Modified Trapezoidal Rule Based On Fzt Amentioning

confidence: 99%