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Article
Lie Symmetries and Partial Differential Equations(PDEs)

Author: Samar kadhum Al-Nassar
Journal: Univesity of Thi-Qar Journal مجلة جامعة ذي قار العلمية ISSN: 66291818 Year: 2016 Volume: 11 Issue: 4 Pages: 1-10
Publisher: Thi-Qar University جامعة ذي قار

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Abstract

There are many well-known techniques for obtaining exact solutions for differential equations, but many of them are simply special cases of a few powerful symmetry methods. Lie symmetry methods are techniques for finding exact solutions of a wide variety of differential equations. In this paper, we discuss the use of Lie symmetries on PDEs of order two in two independent variables and show how they can be used to transform the governing equation into another equation with one less independent variable. In addition, for our case study we consider the PDE(the bond-pricing equation) and solve the equation using Lie symmetry methods.

هناك العديد من التقنيات المعروفة للحصول على حلول دقيقة للمعادلات التفاضلية ، ولكن الكثير منهم مجرد حالات خاصة من عدد قليل من طرق التناظر القوية. تناظرات لي هي تقنيات لإيجاد الحلول الدقيقة لمجموعة واسعة من المعادلات التفاضلية. في هذا البحث نناقش استخدام تناظر لي للمعادلات التفاضلية الجزئية من الدرجة الثانية في اثنين من المتغيرات المستقلة و إظهار الكيفية التي يمكن استخدامها لتحويل المعادلة التفاضلية الجزئية المعطاة الى معادلة اخرى في متغير مستقل واحد. بالاضافة الى ذلك لقد ناقشنا المعادلة التفاضلية الجزئية لسندات التسعير وحلها باستخدام طرق لي للتناظر


Article
A model for non-competitive substrate inhibition in a Bioreactor

Author: Samar Kadhum Al-Nassar
Journal: Journal of Education for Pure Science مجلة التربية للعلوم الصرفة ISSN: 20736592 Year: 2015 Volume: 5 Issue: 2 Pages: 117-141
Publisher: Thi-Qar University جامعة ذي قار

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Abstract

The objective of this study is to learn how to analyse a system of nonlinear differential equations through the techniques of finding their steady states and determining their stability. Also,we learn how to identify the dimensionless groupings in the model in terms of dimensional parameters. In addition, use Maple to solve some problems and plotting the figures, it is very useful. Finally,the objective of this study is to investigate the quality of the effluent leaving the reactor and to investigate the biological reaction of the interaction.


Article
Lie Symmetries to Ordinary Differential Equations (ODEs)

Author: Samar kadhum Al-Nassar
Journal: Journal of Education for Pure Science مجلة التربية للعلوم الصرفة ISSN: 20736592 Year: 2015 Volume: 5 Issue: 1 Pages: 1-18
Publisher: Thi-Qar University جامعة ذي قار

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Abstract

AbstractIn this paper, we have provided some examples motivating the use of Liesymmehies. Also, we have discussed the properties of one- parameter groups oftransformations (Lie groups) and introduced the ideas of invariants of the group oft t"*forro"tio*.In the case of ordinary differential equations use of Lie qmmetriesresulted in a separable ODE when the goveming DE was first order and a reduction oforder when the goveming DE was of order greater tlan one.

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