A new differential quadrature methodology based on Bernstein polynomials and improve ADI-DQM for solving transport equations

العناوين الأخرى

منهجية التفاضل التربيعي الجديد المعتمدة على متعددات حدود برنستين و تحسين ADI-DQM لحل معادلات النقل

مقدم أطروحة جامعية

al-Sadawi, Firas Amir Sadun

مشرف أطروحة جامعية

al-Sayf, Abd al-Sattar Jabir Ali

أعضاء اللجنة

Muhammad, Ali H.
Hawas, Muhammad J.
Muhammad, Ali J.

الجامعة

جامعة البصرة

الكلية

كلية التربية للعلوم الصرفة

القسم الأكاديمي

قسم الرياضيات

دولة الجامعة

العراق

الدرجة العلمية

ماجستير

تاريخ الدرجة العلمية

2013

الملخص الإنجليزي

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.

التخصصات الرئيسية

الرياضيات

عدد الصفحات

85

قائمة المحتويات

• APA
• MLA
• AMA

لغة النص

الإنجليزية

نوع البيانات

رسائل جامعية

رقم السجل

BIM-744197