Boubaker polynomials expansion scheme (BPES) solution to Boltzmann diffusion equation in the case of strongly anisotropic neutral particles forward–backward scattering

Boubaker, K.

doi:10.1016/j.anucene.2011.04.009

Cited by 9 publications

(5 citation statements)

References 22 publications

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“…The Boubaker polynomials that considered in this paper have been established for the first time by Boubaker as a guide for solving a one-dimensional heat transfer equation and second order differential equations [37,38]. There are several papers on these polynomials and their applications in different problems in physics and other computational and applied sciences [39][40][41][42]. The monic Boubaker polynomials are defined as ( B 0 ( ) = 1)…”

Section: Rational Boubaker Functionsmentioning

confidence: 99%

A rational approximation to the boundary layer flow of a non-Newtonian fluid

Parand

Fotouhifar

Yousefi

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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This paper presents a computational technique for the investigation of boundary layer flow over a stretching sheet for a Powell-Eyring non-Newtonian fluid. The quasilinearization method finds a recursive formula for higher-order deformation equations which are then solved using the rational Boubaker collocation method so-called the QLM-RBC method. The solution for velocity is computed by applying the QLM-RBC method. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equations by similarity transformations. The momentum equation with infinite boundary values using the quasilinearization method converts to the sequence of linear ordinary differential equations to obtain the solution. In addition, the equation is solved on a semi-infinite domain without truncating it to a finite domain by choosing rational bases for the collocation method. Illustrative figures are included to demonstrate the physical influence of different parameters on the velocity profile. The method is easy to implement and yields accurate results.

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Section: Rational Boubaker Functionsmentioning

confidence: 99%

A rational approximation to the boundary layer flow of a non-Newtonian fluid

Parand

Fotouhifar

Yousefi

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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“…Taking collocation points as the positive zeros of T 2n (x) we get a system of linear equations for determining the coefficients c m , m = 1,...,n. In the same case r = 1 and μ = 1/π, the corresponding solutions for n = 1 and n = 2, are f (1) 4 (x) = −1.01362B 4 (x) and f…”

Section: Applicationsmentioning

confidence: 99%

“…There are several papers on the so-called Boubaker polynomials and their applications in different problems in physics and other computational and applied sciences (cf. [1,2,3,9] and references therein). Such polynomials are defined in a similar way as Chebyshev polynomials of the first and second kind T n (x) and U n (x), which are orthogonal on (−1, 1) with respect to the weights functions 1/ √ 1 − x 2 and √ 1 − x 2 , respectively.…”

Section: Introductionmentioning

confidence: 99%

Some properties of Boubaker polynomials and applications

Milovanović¹,

Joksimović²

2012

AIP Conference Proceedings

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“…Boubaker polynomials were presented in 2007. These functions were used for solving the Boltzmann diffusion equation Boubaker (2007Boubaker ( , 2011). Love's equation was solved by Kumar via the Boubaker polynomials in Kumar (2010).…”

Section: Introductionmentioning

confidence: 99%

An approach to solve fractional optimal control problems via fractional-order Boubaker wavelets

Rabiei

Razzaghi

2022

Journal of Vibration and Control

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This work is devoted to numerical solution to solve fractional optimal control problems (FOCPs). The fractional-order Boubaker wavelets (FOBWs) are introduced. By applying hypergeometric functions, an exact formula for Riemann–Liouville fractional integral operator for FOBW is obtained. By using this formula, the FOCP is reduced into a corresponding optimization problem which can be solved by applying the Lagrange multiplier method. Also, the convergence for the present method is provided. Seven numerical examples are included to demonstrate the applicability of the proposed technique. In Example 6, it will be shown that we can achieve the exact solutions which were not obtained previously in the literature. In addition, in Example 7, a practical example in a cancer model is provided.

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Boubaker polynomials expansion scheme (BPES) solution to Boltzmann diffusion equation in the case of strongly anisotropic neutral particles forward–backward scattering

Cited by 9 publications

References 22 publications

A rational approximation to the boundary layer flow of a non-Newtonian fluid

A rational approximation to the boundary layer flow of a non-Newtonian fluid

Some properties of Boubaker polynomials and applications

An approach to solve fractional optimal control problems via fractional-order Boubaker wavelets

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