May 23, 2012 comment on a dynamical model for investigation of a 3 point maximal spatial evolution during resistance spot welding using boubaker polynomials by s. On the connection coefficients of the chebyshevboubaker. Some properties of boubaker polynomials and applications. A polynomial of degree one is called a linear polynomial. A boubaker polynomials expansion scheme bpesrelated study of metaloxides functional materials conjoint roughnesshardness properties materials science and engineering. In this paper, we focus on boubaker polynomials in fractional calculus area and obtain the operational matrix of caputo fractional derivative and the operational matrix of the riemannliouville fractional integration for the first time.
Read properties of boubaker polynomials and an application to loves integral equation, applied mathematics and computation on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. This paper is organized into following sections of which this introduction is the. Enter your mobile number or email address below and well send you a link to download the free kindle app. This scheme is a resolution protocol which has been successfully applied to several applied physics and mathematics problems. A numerical approach for solving linear integrodifferential. Recently, the mboubaker polynomials modified boubaker polynomials have been defined as an ameliorated form that was more appropriated for defining a characteristic differential equation4. Solution to heat equation inside cryogenic vessels using. Unlike in most classical works, the effects of viscous dissipation which is coupled with the temperaturedependent thermal diffusivity are considered in the energy equation. Using the language of riordan arrays, we study a oneparameter family of orthogonal polynomials that we call the restricted. Some properties of boubaker polynomials and a pplications. A numerical approach for solving linear integrodifferentialdifference equations with boubaker polynomial bases. The comparative boubaker polynomials expansion scheme bpes. Solutions to several applied physics problems based on the socalled.
Pdf on the connection coefficients of the chebyshev. A boubaker polynomials expansion scheme solution to random loves equation in the case of a rational kernel m. In the last decades, these two techniques have been separately performed for obtaining accurate numerical solutions to several initial boundary value problems vo. Review a numerical approach for solving linear integrodi. Computersandmathematicswithapplications622011536538 contents lists available at sciencedirect computersandmathematicswithapplications journal homepage. A numerical approach for solving linear integrodifferentialdifference equations with boubaker polynomial bases 155. In section 2, we introduce mathematical formulation. Boubaker polynomials have generated many integer sequences in the w. The chebyshev boubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary riordan arrays. Boubaker polynomials pdf the paper deals with threeterm recurrence relations for boubaker and related polynomials, as well as some properties including zero. Boubaker polynomials collocation approach for solving. Pdf fermatlinked relations for the boubaker polynomial.
Boubaker polynomials and their applications to numerical solution. The boubaker polynomials were established for the first time by boubaker 1, 5, 6 as a guide for solving a onedimensional heat transfer. The paper is also cited in this 2015 in press publication. Boubaker hybrid functions and their application to solve. The comparative boubaker polynomials expansion scheme bpes and homotopy perturbation method hpm for solving a standard. Original article fermatlinked relations for the boubaker polynomial sequences via riordan matrices analysis karem boubaker a, lin zhang b, a esstt 63 rue sidi jabeur 5100, mahdia, tunisia b institute of mathematics, hangzhou dianzi university, hangzhou 310037, pr china available online 2 july 2012.
If we do these successfully, we find that we have mastered the basics of the topic. Fractionalorder boubaker functions and their applications in. The comparative boubaker polynomials expansion scheme. Using riordan matrices analysis, a sequence of relations outlining the relations with chebyshev and fermat polynomials have been obtained. Mohsen torabi, hessameddin yaghoobi, karem boubaker. Files are available under licenses specified on their description page. All structured data from the file and property namespaces is available under the creative commons cc0 license. By this transform, the spectraltype numerical method using boubaker. Section 2 deals with some properties of boubaker polynomials. Temperature 3d profiling in cryogenic cylindrical devices using boubaker polynomials expansion scheme bpes. The boubaker polynomials are investigated in this paper. For a complex function fx of a real argument x defined in the domain.
The aim of this approach is converting the multiorder fde into a set of algebraic. Pdf the boubaker polynomials are investigated in this paper. Temperature variations analysis for condensed matter micro. Boubaker polynomials collocation approach for solving systems of. Original article analytical approximation for landaus constants by using the boubaker polynomials expansion scheme method lin zhang a, karem boubaker b a institute of mathematics, hangzhou dianzi university, hangzhou 310018, pr china. The boubaker polynomials, a new function class for solving bivaried second order differential equations, f. The boubaker polynomials were established and discussed in several previous studies, as a polynomial sequence related to a solution to the heat transfer equation in a special model of a vertical. In each section we are led, after a brief introduction, into a sequence of problems on a certain topic. Comment on a dynamical model for investigation of a 3 point maximal spatial evolution during resistance spot welding using boubaker polynomials by s. The boubaker polynomials and their application to solve.
Pdf some properties of boubaker polynomials and applications. Heat transfer of pseudoplastic powerlaw nonnewtonian fluids aligned with a semiinfinite plate is studied. Kumar used these polynomials to solve loves equation in a particular physical system. A boubaker polynomials expansion scheme solution to. Oct 11, 2018 a new hybrid of blockpulse functions and boubaker polynomials is constructed to solve the inequality constrained fractional optimal control problems focps with quadratic performance index and fractional variational problems fvps. In this paper, we present a spectrallike method with boubaker polynomials to solving numerically some differential equations. In this paper, a new collocation method, which is based on boubaker polynomials, is introduced for the approximate solutions of mixed linear integro. A new hybrid of blockpulse functions and boubaker polynomials is constructed to solve the inequality constrained fractional optimal control problems focps with quadratic performance index and fractional variational problems fvps. Analytic solutions were given and compared with the numerical results for some real powerlaw index and the unsteadiness. Fermatlinked relations for the boubaker polynomial sequences. Boubaker polynomials expansion schemerelated heat transfer.
A numerical approach for solving optimal control problems. Analytical approximation for landauas constants by using. The paper is also cited in this in press publication. Boubaker polynomial spectrallike method for numerical solution of. Temperature 3d profiling in cryogenic cylindrical devices using boubaker polynomials expansion scheme bpes author links open overlay panel b. A boubaker polynomials expansion scheme bpesrelated study of metaloxides functional materials conjoint roughnesshardness properties. Equivalently, these determinant formulas may be also rewritten as combinatorial identities involving sum of products of boubaker polynomials and multinomial coefficients. In this paper, the flow of a powerlaw fluid film on an unsteady stretching surface is analyzed by the means of boubaker polynomials expansion scheme bpes.
Combinatorial determinant formulas for boubaker polynomials. The resolution algorithm is mainly based on the boubaker polynomials expansion. A polynomial of degree 1 is called a linear polynomial. Some new features of the boubaker polynomials expansion. Numerical solutions of multiorder fractional differential. We also present new formulas for boubaker polynomials via recurrent threediagonal determinants. The boubaker polynomials expansion scheme for solving. Properties of boubaker polynomials and an application to loves integral equationq gradimir v. Text is available under the creative commons attributionsharealike license. Examples include the chebyshev polynomials of the second kind and the boubaker polynomials. By this transform, the spectraltype numerical method using boubaker polynomial can be deduced for seeking numerical solution of differential equations. We study the connection coefficients of this class of orthogonal polynomials, indicating how riordan array techniques can lead to closedform expressions for these. In this study, we attempt bobuaker extend the already defined the boubaker polynomials that merged from a solution to heat equation. The effects of powerlaw index and the zheng number on the dynamics are analyzed.
Pdf on the connection coefficients of the chebyshevboubaker. Boubaker, a sturmliouville shaped characteristic differential equation as a guide to establish a quasipolynomial expression to the boubaker polynomials, journal of differential equations and c. The boubaker polynomial expansion scheme bpes are also discussed. Polynomials this book uses the medium of problems to enable us, the readers, to educate ourselves in matters polynomial. Boubaker polynomials and their applications to numerical. The chebyshevboubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined. Pdf combinatorial determinant formulas for boubaker. Fermatlinked relations for the boubaker polynomial. Boubaker polynomials collocation approach for solving systems of nonlinear volterrafredholm integral equations. The obtained expressions are a meaningful supply to recent applied physics studies using the boubaker polynomials expansion scheme bpes. Saha raya new numerical approach for the solution of nonlinear fredholm integral equations system. The boubaker polynomials a new function class for solving bi varied second order differential equations. Pdf boubaker polynomials and their applications to. Fermatlinked relations for the boubaker polynomial sequences via riordan matrices analysis karem boubaker a, lin zhang b, a esstt 63 rue sidi jabeur 5100, mahdia, tunisia b institute of mathematics, hangzhou dianzi university, hangzhou 310037, pr china available online 2 july 2012 keywords riordan matrices.
In this paper, we evaluate several families of toeplitzhessenberg determinants whose entries are the boubaker polynomials. Numerical solutions of multiorder fractional differential equations by. After several tests and trials, we set the new proposed polynomials, which are the modified boubaker polynomials defined mainly by eq. The effects of stacking sequences of composite laminated optical beams on free vibration frequencies are investigated using two methods. Then you can start reading kindle books on your smartphone, tablet, or computer no kindle device required. Properties of boubaker polynomials and an application to. Boubaker polynomial spectrallike method for numerical. A boubaker polynomials expansion scheme solution to random. Properties of boubaker polynomials and an application to love. Boubaker polynomials collocation approach for solving systems. A boubaker polynomials expansion scheme solution to random loves equation in the case of a.
On the connection coefficients of the chebyshev boubaker polynomials. The boubaker polynomials are already registered under their final form5. Blubaker more about original research at wikiversity. Some properties of boubaker polynomials and applications gradimir v. You also have studied how to factorise some algebraic expressions.
Notes on uniqueness of the boubaker polynomials expansion. Some differential and analytical properties of the new polynomial issued from an attempt for solving bivaried heat equation, trends appl. Some new properties of the boubaker polynomials expansion scheme are presented in this paper. Pdf some new features of the boubaker polynomials expansion. Mathematical institute of the serbian academy of sciences and arts, knez mihailova 36, p. It is shown in particular that the boubaker polynomials expansion scheme fits standard cauchy boundary conditions. We present a transform from boubaker polynomial to legendre orthogonal polynomials. A transform from boubaker polynomial to shifted legendre orthogonal polynomials is derived. Boubaker polynomialsboubakerlist of papers wikiversity. Pdf combinatorial determinant formulas for boubaker polynomials.
First, the general formulation of the riemannliouville integral operator for boubaker hybrid function is presented for the first time. The discretization method is used to convert the governing partial differential equations into a set of nonlinear. Many approximation and numerical techniques are utilized to determine the numerical solution of multiorder fde 8, 11 the boubaker polynomials were established for the first time by boubaker 1, 5, 6 as a guide for solving a onedimensional heat transfer equation and second order differential equations. A polynomial of degree 2 is called a quadratic polynomial. The chebyshevboubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary riordan arrays. The graphics of first modified boubaker polynomials are presented in fig.
In this paper, boubaker polynomials and the boubaker polynomial expansion scheme bpes are discussed. The problem of an uncompressible powerlaw fluid has long been the challenge in semisolid forming area. Boubaker polynomials expansion scheme bpes the resolution of system and along with boundary conditions has been achieved using the boubaker polynomials expansion scheme bpes 726. International journal of heat and mass transfer 58. Box 367, 11001 beograd, serbia graduate school of business studies, megatrend university, goce del. The comparative boubaker polynomials expansion scheme bpes and homotopy perturbation method hpm for solving a standard nonlinear secondorder boundary value problem. Some properties of boubaker polynomials and applications mi sanu. Dec 27, 2016 in this paper, we focus on boubaker polynomials in fractional calculus area and obtain the operational matrix of caputo fractional derivative and the operational matrix of the riemannliouville fractional integration for the first time. Temperature 3d profiling in cryogenic cylindrical devices. Fractionalorder boubaker functions and their applications. Bouhafs on the higher order derivatives of the 4qboubaker polynomials. Also, a general formulation for the operational matrix of multiplication of these polynomials has been achieved to solve the nonlinear problems. A boubaker polynomials expansion scheme for solving the. Pdf boubaker polynomials and their applications to numerical.
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