Some Results on a Two Variables Pell Polynomials :

Mohammed Abdulhadi  Sarhan; Suha SHIHAB; Mohammed RASHEED

doi:10.29350/qjps.2021.26.1.1246

Mohammed Abdulhadi Sarhan Mathematics Department, College of Sciences, Al-Mustansiriyah University, Baghdad, Iraq,
Suha SHIHAB Applied Sciences Department, University of Technology https://orcid.org/0000-0003-3730-0149
Mohammed RASHEED Applied Sciences Department-University of Technology-Baghdad https://orcid.org/0000-0002-0768-2142

DOI: https://doi.org/10.29350/qjps.2021.26.1.1246

Keywords: Modified second kind Chebyshev polynomials, Operation matrix of derivative, product of two polynomials, differential equations, numerical solutions

Abstract

In this study, Pell polynomials in two variables, and their properties are investigated. Some formulas for two variables Pell polynomials are derived by matrices. By defining special formula for Pell polynomials in one variable, new important properties of Pell polynomials in two variables can be enabled to derive. A new exact formula expressing the partial derivatives of Pell polynomials explicitly of any degree in terms of Pell polynomials themselves is proved. A novel explicit formula, which constructs the two explicit formulas, which construct the two-dimension Pell polynomials expansion coefficients of a first partial derivative of a differentiable function in terms of their original expansion coefficients, is also included in the present article. The main advantage of the presented formulas is that the new properties of Pell polynomials in two variables greatly simplify the original problems and the result will lead to easy calculation of the coefficients of expansion. A direct spectral method along with the presented two variables Pell polynomials is proposed to solve the partial differential equation. Illustrated examples are included to demonstrate the validity of the technique.

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Author Biographies

Suha SHIHAB, Applied Sciences Department, University of Technology

She was born in Baghdad in 1970. He had her B.Sc., M.Sc. degrees in Applied Physics from University of Technology, Baghdad (Iraq) in 27/06/1992, 28/12/1995 respectively, and Ph.D. degree in the College of Science, Al-Mustansiriya University Baghdad (Iraq) in 04/10/2005. He has become a Lecturer in 06/03/1999, Assistant professor at 15/03/2002 and Professor at 02/05/2012. She has research gate h-index 3, Scopus h-index 1 and more than 60 published articles inside, outside Iraq. She supervised on many students (Msc. and PHD.) degrees. He was having a many research group on numerical Analysis, optimal Control Systems, and Mathematical Physics. As well as; She have a group for the characterization of semiconducting thin films and nanostructures materials especially the Optical properties with mathematical models produced by different techniques of preparation such as: Spin Coating and Dip Coating (Sol Gel), Sputtering (DC and RF), PLD, chemical bath deposition (CBD) and ....etc. In addition; I have group for the characterization of Ceramic and Polymer materials mathematically produced by many techniques like solid-state and hydrothermal. Authored more than Five books published it in Lambert Academic Publishing in 2012 in Germany. She is reviewer for many international journals. She participate in more than 12 conferences all of them outside Iraq in France, Romania, Algeria and Tunisia.

Area of Interest:

Applied Mathematics- Advanced Engineering Mathematics- Optimal Control- Optimization- Modeling and Simulation-Numerical Analysis- Integral Equations- Partial and Differential Equations- Applied Physics- Astrophysics- Celestial Mechanics.

Mohammed RASHEED, Applied Sciences Department-University of Technology-Baghdad

Mohammed S. Rasheed: He was born in Baghdad in 1971. He had her B.Sc., M.Sc. degrees in Applied Physics from the University of Technology, Baghdad (Iraq) on 03/09/1992, 17/05/1995 respectively, and a Ph.D. degree from the University of Angers, Angers (France) on 12/12/2017. He has become an Assistant professor at 11\11\2018. He has research gate h-index 3, Scopus h-index 3, and more than 30 published articles inside, outside Iraq, and most of them in Clarivate journals. He was having a many research groups on the Preparation and characterization of semiconducting thin films and nanostructures produced by the Spin Coating and Dip Coating (Sol-Gel) technique. As well, He is a member of research groups on the preparation and characterization of semiconducting thin films by chemical bath deposition (CBD) and preparation and characterization of Ceramic and Polymer materials produced by many techniques like solid-state and hydrothermal. Authored one book on the laser communication system and published it in Lambert Academic Publishing in 2012 in Germany. He is a reviewer for two international journals indexed in (Springer & Elsevier). He participates in more than 12 conferences all of them outside Iraq in France, Romania, Algeria, and Tunisia.

Some Results on a Two Variables Pell Polynomials

Applied Mathematics

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