Approximate solution of two-dimensional Sobolev equation using a mixed Lucas and Fibonacci polynomials

Funding informationThere are no funders to report for this submission.Fascioliasis is a liver fluke disease in which food and water are the transmitting agents. The disease is caused by a genus of Fasciola, parasitic Trematoda. The genus Fasciola includes two species of Fasciola gigantica and Fasciola hepatica.The study of this disease is of particular importance as the infected cases are globally growing, especially in endemic areas. In this paper, a fractional-order mathematical model is presented for fascioliasis disease. The optimization method is an effective choice in solving mathematical models of epidemic diseases. The study aims at presenting a new set of generalized Fibonacci polynomials as basic functions and some innovative operational matrices of derivatives in the Caputo sense to solve the fascioliasis disease model. The numerical experiments reveal better results and simulations show effectiveness of the presented method.

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“…The Fibonacci polynomials are defined by a recurrence relation 17–26

F_{n} false(t false) = ({, \begin{matrix} left leftarray \\ array 0, & array n = 0, \\ array 1, & array n = 1, \\ array t F_{n - 1} (t) + F_{n - 2} (t), & array n \geq 2 . \end{matrix})

…”

Section: Required Toolsmentioning

confidence: 99%

Optimal study on fractional fascioliasis disease model based on generalized Fibonacci polynomials

Avazzadeh

Hassani

Agarwal

et al. 2023

Math Methods in App Sciences

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“…Mirzae and Hoseini solved singularly perturbed differential-difference equations arising in science and engineering with Fibonacci polynomials in [21]. Also, in [22], Haq et al studied approximate solution of two-dimensional Sobolev equation using a mixed Lucas and Fibonacci polynomials.…”

Section: Diskaya Et Al Created a New Encryption Algorithm (Known As Aes-like) By Using The Aes Algorithm Inmentioning

confidence: 99%

k-Order Fibonacci Polynomials on AES-Like Cryptology

Asci¹,

Aydınyüz²

2022

Computer Modeling in Engineering &Amp; Sciences

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The Advanced Encryption Standard (AES) is the most widely used symmetric cipher today. AES has an important place in cryptology. Finite field, also known as Galois Fields, are cornerstones for understanding any cryptography. This encryption method on AES is a method that uses polynomials on Galois fields. In this paper, we generalize the AES-like cryptology on 2 × 2 matrices. We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm. So, this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix.

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“…There are lots of numerical methods to solve the heat conduction equation, such as several finite difference schemes (FDM) [5][6][7], finite element methods (FEM) [8], or a combination of these [9]. However, they can be computationally demanding since they require the full spatial discretization of the examined system.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of Explicit and Stable Time Integration Schemes for Heat Conduction in an Insulated Wall

2022

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Calculating heat transfer in building components is an important and nontrivial task. Thus, in this work, we extensively examined 13 numerical methods to solve the linear heat conduction equation in building walls. Eight of the used methods are recently invented explicit algorithms which are unconditionally stable. First, we performed verification tests in a 2D case by comparing them to analytical solutions, using equidistant and non-equidistant grids. Then we tested them on real-life applications in the case of one-layer (brick) and two-layer (brick and insulator) walls to determine how the errors depend on the real properties of the materials, the mesh type, and the time step size. We applied space-dependent boundary conditions on the brick side and time-dependent boundary conditions on the insulation side. The results show that the best algorithm is usually the original odd-even hopscotch method for uniform cases and the leapfrog-hopscotch algorithm for non-uniform cases.

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Approximate solution of two-dimensional Sobolev equation using a mixed Lucas and Fibonacci polynomials

Cited by 20 publications

References 33 publications

Optimal study on fractional fascioliasis disease model based on generalized Fibonacci polynomials

Optimal study on fractional fascioliasis disease model based on generalized Fibonacci polynomials

k-Order Fibonacci Polynomials on AES-Like Cryptology

A Comparative Study of Explicit and Stable Time Integration Schemes for Heat Conduction in an Insulated Wall

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