Partial Differential Equation Exact Solutions Using Lie Group Classifications

الموضوعات

علوم تطبيقية وتكنولوجية

الملخص

Nonlinear Partial Differential Equations (PDEs) are one of the key area of the interaction of mathematics and other sciences. Most physical phenomena can be described by (PDEs). Many methods of mathematical physics have been developed to solve differential equations, among which Lie group method is an area of mathematics in which we can see a harmonious interaction between the methods of classical analysis and modern algebra. The objective of the research is to obtain the Lie symmetries and the exact solutions of nonlinear partial differential equations, which represent example of the important physical phenomena. The study of these systems of differential equations is often regarded as a difficult and confusing endeavor due to various limitations. The study deal with the methods of group invariant solutions, through the constructive procedures Lie established that, in the case of (ODEs), invariance under one-parameter symmetry group implies that the order of the equation can be reduced by one. The main tool in this study will be Lie classical method for reduction (PDEs) and other method including hyperbolic secant-tangent functions expansion method for some exact solutions of (ODEs). The study considers the regulaised long wave to apply the method. Among which Lie group method is an efficient approach to derive the exact solution of nonlinear partial differential equations and it's easy method that depends on solution of algebra equations. The study recommends that Lie group can be applied to other nonlinear partial differential equations. Computer program could be used in the method of solution, especially in the solution of (ODEs) in order to simplify the process of a solution.

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التعريف والنوع

رقم الوثيقة

0387245e-4032-422c-98d1-b11d27496554

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل ماجيستير

نوع الملف

pdf text

أسماء الملفات

72375_1.pdf

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ألقاب المؤلفين

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اللغة

English

المصدر والدورية

اسم المصدر

Partial Differential Equation Exact Solutions Using Lie Group Classifications

المحتوى والصفحات

عدد الصفحات

0

إشراف وإعداد

الإشراف

عبد الرحيم بشير حامد, عماد الدين عبدالله عبد الرحيم

الإعداد

منال أحمد إبراهيم الأمين

الاقتباسات الببليوغرافية