Fuzzy finite difference method for solving fuzzy Poisson’s equation

Abdi, Mohammad Javad; Allahviranloo, Tofigh

doi:10.3233/jifs-190408

Cited by 3 publications

(3 citation statements)

References 19 publications

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“… 35 – 40 : Let I be a real interval. A mapping is called a fuzzy process, defined as and The derivative of a fuzzy process is defined by …”

Section: Fuzzy Analysismentioning

confidence: 99%

“…FDEs on the nth order differential equation with fuzzy initial conditions were applied by Buckley and Feuring 38 , 39 . FDE was utilized by Abdi and Allahviranloo 40 to solve the fuzzy Poisson's equation with fuzzy Dirichlet boundary conditions using the fuzzy finite difference method (FFDM). With the use of double parametric FN, Almutairi et al 41 derived the numerical solution of the fuzzy wave equation.…”

Section: Introductionmentioning

confidence: 99%

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Numerical analysis of a second-grade fuzzy hybrid nanofluid flow and heat transfer over a permeable stretching/shrinking sheet

Nadeem

Siddique

Awrejcewicz

et al. 2022

Sci Rep

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In this work, the heat transfer features and stagnation point flow of Magnetohydrodynamics (MHD) hybrid second-grade nanofluid through a convectively heated permeable shrinking/stretching sheet is reported. The purpose of the present investigation is to consider hybrid nanofluids comprising of Alumina $$\left( {{\text{Al}}_{{2}} {\text{O}}_{{3}} } \right)$$ Al 2 O 3 and Copper $$\left( {{\text{Cu}}} \right)$$ Cu nanoparticles within the Sodium Alginate (SA) as a host fluid for boosting the heat transfer rate. Also, the effects of free convection, viscous dissipation, heat source/sink, and nonlinear thermal radiation are considered. The converted nonlinear coupled fuzzy differential equations (FDEs) with the help of triangular fuzzy numbers (TFNs) are solved using the numerical scheme bvp4c. The numerical results are acquired for various engineering parameters to study the Nusselt number, skin friction coefficient, velocity, and temperature distribution through figures and tables. For the validation, the current numerical results were found to be good as compared to existing results in limiting cases. It is also inspected by this work that with the enhancement of the volume fraction of nanoparticles, the heat transfer rate also increases. So, it may be taken as a fuzzy parameter for a better understanding of fuzzy variables. For the comparison, the volume fraction of nanofluids and hybrid nanofluid are said to be TFN [0, 0.1, 0.2]. In the end, we can see that fuzzy triangular membership functions (MFs) have not only helped to overcome the computational cost but also given better accuracy than the existent results. Finding from fuzzy MFs, the performance of hybrid nanofluids is better than nanofluids.

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“… 35 – 40 : Let I be a real interval. A mapping is called a fuzzy process, defined as and The derivative of a fuzzy process is defined by …”

Section: Fuzzy Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical analysis of a second-grade fuzzy hybrid nanofluid flow and heat transfer over a permeable stretching/shrinking sheet

Nadeem

Siddique

Awrejcewicz

et al. 2022

Sci Rep

View full text Add to dashboard Cite

show abstract

“…It was found that the solution of the fuzzy heat equation with a small fuzzy number area provides more accurate results than the large area. Abdi and Allahviranloo [9] implemented the finite difference method to solve the fuzzy Poisson's equation with Dirichlet boundary conditions. The convergence of the proposed method was investigated and a numerical example was solved for more illustration of the proposed approach.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Numerical Solution via Finite Difference Scheme of Wave Equation in Double Parametrical Fuzzy Number Form

et al. 2021

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The use of fuzzy partial differential equations has become an important tool in which uncertainty or vagueness exists to model real-life problems. In this article, two numerical techniques based on finite difference schemes that are the centered time center space and implicit schemes to solve fuzzy wave equations were used. The core of the article is to formulate a new form of centered time center space and implicit schemes to obtain numerical solutions fuzzy wave equations in the double parametric fuzzy number approach. Convex normalized triangular fuzzy numbers are represented by fuzziness, based on a double parametric fuzzy number form. The properties of fuzzy set theory are used for the fuzzy analysis and formulation of the proposed numerical schemes followed by the new proof stability thermos under in the double parametric form of fuzzy numbers approach. The consistency and the convergence of the proposed scheme are discussed. Two test examples are carried out to illustrate the feasibility of the numerical schemes and the new results are displayed in the forms of tables and figures where the results show that the schemes have not only been effective for accuracy but also for reducing computational cost.

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Dynamical behaviors of a k-order fuzzy difference equation

Han

et al. 2022

Open Mathematics

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Difference equations are often used to create discrete mathematical models. In this paper, we mainly study the dynamical behaviors of positive solutions of a nonlinear fuzzy difference equation: x n + 1 = x n A + B x n − k ( n = 0 , 1 , 2 , … ) , {x}_{n+1}=\frac{{x}_{n}}{A+B{x}_{n-k}}\hspace{0.33em}\left(n=0,1,2,\ldots ), where parameters A , B A,B and initial value x − k , x − k + 1 , … , x − 1 , x 0 {x}_{-k},{x}_{-k+1},\ldots ,{x}_{-1},{x}_{0} , k ∈ { 0 , 1 , … } k\in \{0,1,\ldots \} are positive fuzzy numbers. We investigate the existence, boundedness, convergence, and asymptotic stability of the positive solutions of the fuzzy difference equation. At last, we give numerical examples to intuitively reflect the global behavior. The conclusion of the global stability of this paper can be applied directly to production practice.

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Fuzzy finite difference method for solving fuzzy Poisson’s equation

Cited by 3 publications

References 19 publications

Numerical analysis of a second-grade fuzzy hybrid nanofluid flow and heat transfer over a permeable stretching/shrinking sheet

Numerical analysis of a second-grade fuzzy hybrid nanofluid flow and heat transfer over a permeable stretching/shrinking sheet

Fuzzy Numerical Solution via Finite Difference Scheme of Wave Equation in Double Parametrical Fuzzy Number Form

Dynamical behaviors of a k-order fuzzy difference equation

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