An analytical solution to applied mathematics-related Love’s equation using the Boubaker polynomials expansion scheme

Kumar, Anil

doi:10.1016/j.jfranklin.2010.08.008

Cited by 57 publications

(38 citation statements)

References 29 publications

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“…where B 4k are the 4k-order Boubaker polynomials [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], r k are B 4k minimal positive roots, N 0 is a prefixed integer, and ξ k | k=1,...,N0 are unknown pondering real coefficients. This expression refers to the Boubaker polynomials expansion scheme (BPES) [29][30][31].…”

Section: Governing Equationsmentioning

confidence: 99%

A Model for Conjoint Shape Memory and Pseudo-Elastic Effects during Martensitic Transformation

Boubaker

2012

ISRN Metallurgy

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Shape memory alloys (SMA) are metals which can restore their initial shape after having been subjected to a deformation. They exhibit in general both nonlinear shape memory and pseudoelastic effects. In this paper, shape memory alloy (SMA) and its constitutive model with an empirical kinetics equation are investigated. A new formulation to the martensite fractiondependent Young modulus has been adopted and the plastic deformation was taken into account. To simulate the variations, a one-dimensional constitutive model was constructed based on the uniaxial tension features.

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Section: Governing Equationsmentioning

confidence: 99%

A Model for Conjoint Shape Memory and Pseudo-Elastic Effects during Martensitic Transformation

Boubaker

2012

ISRN Metallurgy

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“…The Boubaker Polynomials Expansion Scheme (BPES) [26][27][28][29][30][31][32][33][34][35] is a resolution protocol which has been successfully applied to several applied physics and mathematics problems. The BPES protocol ensures the validity of the related boundary conditions regardless main equation features.…”

Section: The Boubaker Polynomials Expansion Scheme (Bpes)mentioning

confidence: 99%

“…Several solution have been proposed through the BPES in many fields such as numerical analysis [26], material characterization [27], theoretical physics [28], mathematical algorithms [29], heat transfer [31,32], and homodynamics [33][34][35].…”

Section: The Boubaker Polynomials Expansion Scheme (Bpes)mentioning

confidence: 99%

A Confirmed Model to Polymer Core-Shell Structured Nanofibers Deposited via Coaxial Electrospinning

Boubaker

2012

ISRN Polymer Science

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A model to core-shell structured polymer nanofibers deposited via coaxial electrospinning is presented. Investigations are based on a modified Jacobi-Gauss collocation spectral method, proposed along with the Boubaker Polynomials Expansion Scheme (BPES), for providing solution to a nonlinear Lane-Emden-type equation. The spatial approximation has been based on shifted Jacobi polynomials P (α,β) T,N (x) with α, β(−1, ∞), T > 0 was n the polynomial degree. The Boubaker Polynomials Expansion Scheme (BPES) main features, concerning the embedded boundary conditions, have been outlined. The modified Jacobi-Gauss points are used as collocation nodes. Numerical examples are included to demonstrate the validity and applicability of the technique, and a comparison is made with existing results. It has been revealed that both methods are easy to implement and yield very accurate results.

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“…The Boubaker polynomials were established for the first time by Boubaker [1,5,6] as a guide for solving a one-dimensional heat transfer equation and second order differential equations. Kumar used these polynomials to solve Love's equation in a particular physical system [14]. We will generalize the operational matrix for fractional integration using Boubaker polynomials [1,5,6,14].…”

Section: Introductionmentioning

confidence: 99%

“…Kumar used these polynomials to solve Love's equation in a particular physical system [14]. We will generalize the operational matrix for fractional integration using Boubaker polynomials [1,5,6,14].…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

2016

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Abstract:In this paper, we have applied a numerical method based on Boubaker polynomials to obtain approximate numerical solutions of multi-order fractional differential equations. We obtain an operational matrix of fractional integration based on Boubaker polynomials. Using this operational matrix, the given problem is converted into a set of algebraic equations. Illustrative examples are are given to demonstrate the efficiency and simplicity of this technique.

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An analytical solution to applied mathematics-related Love’s equation using the Boubaker polynomials expansion scheme

Cited by 57 publications

References 29 publications

A Model for Conjoint Shape Memory and Pseudo-Elastic Effects during Martensitic Transformation

A Model for Conjoint Shape Memory and Pseudo-Elastic Effects during Martensitic Transformation

A Confirmed Model to Polymer Core-Shell Structured Nanofibers Deposited via Coaxial Electrospinning

Numerical solutions of multi-order fractional differential equations by Boubaker polynomials

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