The stability of the Boubaker polynomials expansion scheme (BPES)-based solution to Lotka–Volterra problem

Milgram, A. N.

doi:10.1016/j.jtbi.2010.12.002

Cited by 45 publications

(29 citation statements)

References 14 publications

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“…The Boubaker Polynomials Expansion Scheme BPES (Ghanouchi et al, 2008;Awojoyogbe & Boubaker, 2009;Labiadh & Boubaker, 2007;Slama et al, 2008Slama et al, , 2009Tabatabaei et al, 2009;Fridjine & Amlouk, 2009;Belhadj et al, 2009a;2009b, Barry & Hennessy, 2010Yildirim et al, 2010;Kumar, 2010;Milgram, 2011;Rahmanov, 2011;Benhaliliba et al,2011) is a resolution protocol which has been successfully carried out no several applied-physics and mathematics problems. …”

Section: 2a Fundamentals To the Boubaker Polynomials Expansion Schmentioning

confidence: 99%

Steam gasification of wood biomass in a fluidized biocatalytic system bed gasifier: A model development and validation using experiment and Boubaker Polynomials Expansion Scheme BPES

Vecchione

Moneti

Carlo

et al. 2015

Int. J. Renew. Energy Dev.

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Abstract:One of the most important issues in biomass biocatalytic gasification is the correct prediction of gasification products, with particular attention to the Topping Atmosphere Residues (TARs). In this work, performedwithin the European 7FP UNIfHY project, we develops and validate experimentally a model which is able of predicting the outputs,including TARs, of a steam-fluidized bed biomass gasifier. Pine wood was chosen as biomass feedstock: the products obtained in pyrolysis tests are the relevant model input. Hydrodynamics and chemical properties of the reacting system are considered: the hydrodynamic approach is based on the two phase theory of fluidization, meanwhile the chemical model is based on the kinetic equations for the heterogeneous and homogenous reactions. The derived differentials equations for the gasifier at steady state were implemented MATLAB. Solution was consecutively carried out using the Boubaker Polynomials Expansion Scheme by varying steam/biomass ratio (0.5-1) and operating temperature (750-850°C).The comparison between models and experimental results showed that the model is able of predicting gas mole fractions and production rate including most of the representative TARs compounds.

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Section: 2a Fundamentals To the Boubaker Polynomials Expansion Schmentioning

confidence: 99%

Steam gasification of wood biomass in a fluidized biocatalytic system bed gasifier: A model development and validation using experiment and Boubaker Polynomials Expansion Scheme BPES

Vecchione

Moneti

Carlo

et al. 2015

Int. J. Renew. Energy Dev.

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show abstract

“…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%

“…Several solutions have been proposed through the BPES in many fields such as numerical analysis [28][29][30][31], theoretical physics [31][32][33][34], mathematical algorithms [35], heat transfer [36], homodynamic [37,38], material characterization [39], fuzzy systems modeling [40][41][42], and biology [43,44]. The main advantage of this formulation (9) is the verification of boundary conditions, expressed in (4), in advance to resolution process, along with affording controllable and easy-to-access first derivatives of E(η).…”

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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“…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 stability of the Boubaker polynomials expansion scheme (BPES)-based solution to Lotka–Volterra problem

Cited by 45 publications

References 14 publications

Steam gasification of wood biomass in a fluidized biocatalytic system bed gasifier: A model development and validation using experiment and Boubaker Polynomials Expansion Scheme BPES

Steam gasification of wood biomass in a fluidized biocatalytic system bed gasifier: A model development and validation using experiment and Boubaker Polynomials Expansion Scheme BPES

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

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