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

In this paper, we present a method for the numerical solution of Love's equation in a particular physical system. The resolution protocol is based on the Boubaker Polynomials Expansion Scheme (BPES), followed by array analyses. The obtained results are compared with some recently published ones. The accuracy and the asymptotic behaviors of the solutions are discussed.

[1]  Karem Boubaker,et al.  On Modified Boubaker Polynomials: Some Differential and Analytical Properties of the New Polynomials Issued from an Attempt for Solving Bi-varied Heat Equation , 2007 .

[2]  David Elliott,et al.  A Chebyshev series method for the numerical solution of Fredholm integral equations , 1963, Comput. J..

[3]  Jeffrey S. Reeve,et al.  An efficient parallel version of the householder-QL matrix diagonalisation algorithm , 1999, Parallel Comput..

[4]  Gusmão.  Simple approximation for the Bethe-ansatz solution of the one-dimensional Fermi gas. , 1987, Physical review. B, Condensed matter.

[5]  Andrew G. Glen,et al.  APPL , 2001 .

[6]  Mongi Benhamadou,et al.  On the Gauss, Cholesky and Householder algorithms , 2009, Adv. Eng. Softw..

[7]  R. E. Scraton,et al.  The Solution of Integral Equations in Chebyshev Series , 1969 .

[8]  H. Brakhage.  Über die numerische Behandlung von Integralgleichungen nach der Quadraturformelmethode , 1960 .

[9]  A. T. Bharucha-Reid,et al.  Numerical solutions of random integral equation III: random Chebyshev polynomials and Fredholm equations of the second kind ∗ , 1985 .

[10]  Masaaki Shimasaki,et al.  Numerical solution of integral equations in Chebyshev series , 1973 .

[11]  A. Belhadj,et al.  Boubaker Polynomials Expansion Scheme-Related Heat Transfer Investigation Inside Keyhole Model , 2009 .

[12]  Bo Zhang,et al.  A simple Taylor-series expansion method for a class of second kind integral equations , 1999 .

[13]  K. B. Ben Mahmoud.  Solution to Heat Equation Inside Cryogenic Vessels Using Boubaker Polynomials , 2009 .

[14]  Robert Piessens,et al.  Numerical solution of integral equations of mathematical physics, using Chebyshev polynomials , 1976 .

[15]  S. Fridjine,et al.  A NEW PARAMETER: AN ABACUS FOR OPTIMIZING PV–T HYBRID SOLAR DEVICE FUNCTIONAL MATERIALS USING THE BOUBAKER POLYNOMIALS EXPANSION SCHEME , 2009 .

[16]  L. Fox,et al.  The numerical solution of non-singular linear integral equations , 1953, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[17]  R. Love,et al.  THE ELECTROSTATIC FIELD OF TWO EQUAL CIRCULAR CO-AXIAL CONDUCTING DISKS , 1949 .

[18]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[19]  M. Amlouk,et al.  Enhancement of pyrolysis spray disposal performance using thermal time-response to precursor uniform deposition , 2007 .

[20]  W. Robert Boland,et al.  The numerical solution of Fredholm integral equations using product type quadrature formulas , 1972 .

[21]  E. R. Love.  The potential due to a circular parallel plate condenser , 1990 .

[22]  L. Fox,et al.  Chebyshev polynomials in numerical analysis , 1970 .

[23]  O. Awojoyogbe,et al.  Cut-off cooling velocity profiling inside a keyhole model using the Boubaker polynomials expansion scheme , 2009 .

[24]  J. Bessrour,et al.  Numerical Distribution of Temperature as a Guide to Investigation of Melting Point Maximal Front Spatial Evolution During Resistance Spot Welding Using Boubaker Polynomials , 2009 .

[25]  T. Corle,et al.  The circular parallel plate capacitor: a numerical solution for the potential , 1985 .

[26]  Maurice Clint,et al.  Recursive least-squares using a hybrid Householder algorithm on massively parallel SIMD systems , 1999, Parallel Comput..

[27]  Dianne P. O'Leary,et al.  Parallel QR factorization by Householder and modified Gram-Schmidt algorithms , 1990, Parallel Comput..

[28]  Karem Boubaker,et al.  A solution to Bloch NMR flow equations for the analysis of hemodynamic functions of blood flow system using m-Boubaker polynomials , 2009 .

[29]  V. Thangaraj,et al.  Numerical solution of random love's integral equation , 1988 .

[30]  B. M. Fulk.  MATH , 1992 .