Numerical solution of partial differential equations with the help of fuzzy transform technique

Holčapek, Michal; Valášek, Radek

doi:10.1109/fuzz-ieee.2017.8015742

Cited by 4 publications

(4 citation statements)

References 9 publications

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“…, M − 1. It is important to stress that Equation (21) with unknown function V +1 and two boundary conditions (23) and (24) is a two point boundary value problem. Therefore, we apply the proposed above GFPP method for finding its numerical solution.…”

Section: Real-life Applicationmentioning

confidence: 99%

“…Below, we consider the European put option problem [23] as a particular case of Black-Scholes equation (17) with the following boundary and initial conditions:…”

Section: Real-life Applicationmentioning

confidence: 99%

“…where r = 0.0176, σ = 0.4594, T = 1/3, K = 4000 (strike price (Euro)) and S max = 4K. The analytic form of the solution to this problem is known and given in [23] as follows:…”

Section: Real-life Applicationmentioning

confidence: 99%

See 2 more Smart Citations

F-Transform Inspired Weak Solution to a Boundary Value Problem

Nguyen

Perfilieva

Holčapek

2019

Axioms

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We propose and show efficiency of a new fuzzy-transform-based numerical method of solving ordinary differential equations with boundary conditions. The focus is on weak solutions and a special construction of a two-parameterized family of test functions. On theoretical and computational levels, we show how the proposed technique relates to and outperforms the Ritz–Galerkin method. We emphasize the importance of the proposed technique by considering its application to a real-life problem—the option pricing policy.

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Section: Real-life Applicationmentioning

confidence: 99%

“…Below, we consider the European put option problem [23] as a particular case of Black-Scholes equation (17) with the following boundary and initial conditions:…”

Section: Real-life Applicationmentioning

confidence: 99%

See 1 more Smart Citation

F-Transform Inspired Weak Solution to a Boundary Value Problem

Nguyen

Perfilieva

Holčapek

2019

Axioms

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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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Dimensionality Reduction by Fuzzy Transforms with Applications to Mathematical Finance

Perfilieva

2017

Econometrics for Financial Applications

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Numerical solution of partial differential equations with the help of fuzzy transform technique

Cited by 4 publications

References 9 publications

F-Transform Inspired Weak Solution to a Boundary Value Problem

F-Transform Inspired Weak Solution to a Boundary Value Problem

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

Dimensionality Reduction by Fuzzy Transforms with Applications to Mathematical Finance

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