STRUM-LIOUVILLE FORM AND OTHER IMPORTANT PROPERTIES OF MODIFIED ORTHOGONAL BOUBAKER POLYNOMIALS

Authors:

Nazeer Ahmed Khoso,Muhammad Mujtaba Shaikh,Abdul Wasim Shaikh,

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00007

Keywords:

Recurrence relation, Rodriguez’s formula, Orthogonality, Strum-Liouville form.,Rodriguez’s formula,Orthogonality,Strum-Liouville form,

Abstract

In this paper, some classical properties of modified orthogonal Boubaker polynomials (MOBPs) are considered, which are: the three-term recurrence relation, Rodriguez formula, characteristic differential equation and the Strum-Liouville form. The only properties of the MOBPs known so far are orthogonality evidence, weight function, orthonormality evidence and zeros. The new properties established in this work will to the applicability of the MOBPs in different areas of science and engineering where the classical non-orthogonal Boubaker polynomials could be applied, and even in cases where these cannot be applied.   

Refference:

I. Abramowitz, M. and Stegun, I. A. (Eds.). “Orthogonal Polynomials.” Ch. 22 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 771-802, 1972.
II. Ahmed, I. N. (2020). Numerical Solution for Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials. Emirates Journal for Engineering Research, 25(2), 4.
III. Boubaker, K. (2007). On modified Boubaker polynomials: some differential and analytical properties of the new polynomials issued from an attempt for solving bi-varied heat equation. Trends in Applied Sciences Research, 2(6), 540-544
IV. Boubaker, K., Chaouachi, A., Amlouk, M., & Bouzouita, H. (2007). Enhancement of pyrolysis spray disposal performance using thermal time-response to precursor uniform deposition. The European Physical Journal-Applied Physics, 37(1), 105-109.
V. Chew, W. C., & Kong, J. A. (1981, March). Asymptotic formula for the capacitance of two oppositely charged discs. In Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 89, No. 2, pp. 373-384). Cambridge University Press.
VI. Dada, M., Awojoy ogbe, O. B., Hasler, M. F., Mahmoud, K. B. B., & Bannour, A. (2008). Establishment of a Chebyshev-dependent inhomogeneous second order differential equation for the applied physics-related Boubaker-Turki polynomials. Applications and Applied Mathematics: An International Journal, 3(2), 329-336.
VII. Dubey, B., Zhao, T.G., Jonsson, M., Rahmanov, H., 2010. A solution to the accelerated-predator-satiety Lotka–Volterra predator–prey problem using Boubaker polynomial expansion scheme. J. Theor. Biol. 264 (1), 154–160.
VIII. Khoso, N. A., Shaikh, M. M., Shaikh A. W. (2020) “On orthogonalization of Boubaker polynomials”, Journal of Mechanics of Continua and Mathematical Sciences, Vo. 15, No. 11, 119-131.
IX. Labiadh, H., & Boubaker, K. (2007). A Sturm-Liouville shaped characteristic differential equation as a guide to establish a quasi-polynomial expression to the Boubaker polynomials. Дифференциальные уравнения и процессы управления, (2), 117-133.
X. Orthogonal polynomials, Encyclopedia of Mathematics, EMS Press, 2001 [1994]
XI. Ouda, E. H., Ibraheem, S. F., & Fahmi, I. N. A. (2016). Indirect Method for Optimal Control Problem Using Boubaker Polynomial. Baghdad Science Journal, 13, 1.
XII. Shaikh, M. M., & Boubaker, K. (2016). An efficient numerical method for computation of the number of complex zeros of real polynomials inside the open unit disk. Journal of the Association of Arab Universities for Basic and Applied Sciences, 21(1), 86–91.
XIII. Slama, S., Bessrour, J., Boubaker, K., Bouhafs, M., 2008b. A dynamical model for investigation of A3 point maximal spatial evolution during resistance spot welding using Boubaker polynomials. Eur. Phys. J. Appl. Phys. 44 (03), 317–322.
XIV. Yücel, U. (2010). The Boubaker Polynomials Expansion Scheme for Solving Applied-physics Nonlinear high-order Differential Equations. Studies in Nonlinear Science, 1(1), 1-7.

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