A new differential quadrature methodology based on Bernstein polynomials and improve ADI-DQM for solving transport equations
Other Title(s)
منهجية التفاضل التربيعي الجديد المعتمدة على متعددات حدود برنستين و تحسين ADI-DQM لحل معادلات النقل
Dissertant
Thesis advisor
al-Sayf, Abd al-Sattar Jabir Ali
Comitee Members
Muhammad, Ali H.
Hawas, Muhammad J.
Muhammad, Ali J.
University
University of Basrah
Faculty
College of Education for Pure Sciences
Department
Department of Mathematics
University Country
Iraq
Degree
Master
Degree Date
2013
English Abstract
In this thesis, we propose a new technique of the differential quadrature method to find numerical solutions of the different transport (convection-diffusion) equations with appropriate initial and boundary conditions.
The present method is based on the Bernstein polynomials formula, which is used to construct the weighting coefficients matrices of differential quadrature method, the new methodology is called Bernstein differential quadrature method.
To demonstrate the usefulness and accuracy of our suggestion, BDQM are applied to four test problems, involving different linearity.
The numerical results that were obtained by using BDQM, proved that it have high accuracy, good convergence and a reasonable stability with few grid points.
These facts are reported in tables and figures, which represented the numerical solutions of the transport problems in this study.
Also, we improved alternating direction implicit formulation of differential quadrature method (ADI-DQM) that presented by (Al-Saif and Al-Kanani (2011-2013)), based on Bernstein differential quadrature method (ADI-BDQM) for solving transport (convection-diffusion) equations.
The improved technique is then tested by numerical examples.
Results show that the convergence of the new scheme is faster and the solutions are much more accurate than those obtained with the other methods.
Also, the new scheme has reasonable stability.
Besides, comparison the numerical results for ADI-BDQM and BDQM with the available results in the other numerical methods that proved to the efficiency and accuracy our proposals.
The results show that the differential quadrature technique renewed can be used as a powerful, reliable, accurate and efficient numerical tool in solving the transport problems.
Main Subjects
No. of Pages
85
Table of Contents
Table of contents.
Abstract.
Abstract in Arabic.
Chapter One : General introduction.
Chapter Two : The differential quadrature method and weighting coefficients.
Chapter Three : Bernstein differential quadrature method for solving the unsteady state transport equations.
Chapter Four : An improved ADI-DQM based on bernstein polynomials for solving two-dimensional transport equations.
Chapter Five : Errors and stability analysis.
Conclusions and future works.
References.
American Psychological Association (APA)
al-Sadawi, Firas Amir Sadun. (2013). A new differential quadrature methodology based on Bernstein polynomials and improve ADI-DQM for solving transport equations. (ماجستير Theses and Dissertations Master). جامعة البصرة, Iraq
https://search.emarefa.net/detail/BIM-744197
Modern Language Association (MLA)
al-Sadawi, Firas Amir Sadun. A new differential quadrature methodology based on Bernstein polynomials and improve ADI-DQM for solving transport equations. (ماجستير Theses and Dissertations Master). جامعة البصرة. (2013).
https://search.emarefa.net/detail/BIM-744197
American Medical Association (AMA)
al-Sadawi, Firas Amir Sadun. (2013). A new differential quadrature methodology based on Bernstein polynomials and improve ADI-DQM for solving transport equations. (ماجستير Theses and Dissertations Master). جامعة البصرة, Iraq
https://search.emarefa.net/detail/BIM-744197
Language
English
Data Type
Arab Theses
Record ID
BIM-744197
