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Register a new userNumerical Solution of Some Important Models of Partial Differential Equations Using Approximate - Analytical Methods ( ADM – VIM )
الحل العددي لبعض النماذج الهامة من المعادلات التفاضلية الجزئية باستخدام طرائق تقريبية – تحليلية (ADM-VIM)
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تركز بحثنا في هذه المقالة على دراسة طريقتي ADM – VIM و استخداميما لحل بعض النماذج الهامة من المعادلات التفاضلية الجزئية الخطية و غير الخطية مثل ( معادلة كلاين غوردن غير الخطية – معادلة الموجة غير الخطية – معادلة التلغراف الخطية – معادلة انتشار الحرارة غير الخطية )، و قد حصلنا على الحل الفعلي للمسائل المدروسة من أجل تكرارات متعددة، و قمنا بإجراء دراسة عددية عند تكرار محدد ثم قارنا الطريقتين السابقتين مع الحل الفعلي أثناء حلنا لمعادلة التلغراف و معادلة الحرارة غير الخطية، و أيضا أجرينا مقارنة بين الحل الفعلي و الحل بطريقة ADM (من أجل تكرار محدد ) لمعادلة كلاين غوردن غير الخطية، ثم قارنا بين الحل الفعلي و الحل بطريقة VIM لمعادلة الموجة غير الخطية، و في جميع الحالات حصلنا على نتائج دقيقة و فعالة أثبتت دقة و قوة و فعالية الطريقتين المدروستين .
In this article, powerful approximate analytical methods, called Adomian decomposition method and variational iteration method are introduced and applied to obtaining the approximate analytical solutions for an important models of linear and non-linear partial differential equations such as ( nonlinear Klein Gordon equation - nonlinear wave equation - linear telegraph equation - nonlinear diffusion convection equation ) . The studied examples are used to reveal that those methods are very effective and convenient for solving linear and nonlinear partial differential equations . Numerical results and comparisons with the exact solution are included to show validity, ability, accuracy, strength and effectiveness of those techniques.
References used
ABASSY ,T 2012 - Modified variational iteration method (non-homogeneous initial value problem) . Mathematical and Computer Modelling . Vol .55, 1222-1232p
ABDELRAZEC , A.H.M . 2008 - Adomian Decomposition Method : Convergence Analysis and Numerical Approximations . McMaster University , Canada , 58p
ALAO ,S ., AKINBORO , F. S.,AKINPELU , F.O. & ODERINU ,R .A. 2014 - Numerical Solution of Integro- Differential Equation Using Adomian Decomposition and Variational Iteration Methods . IOSR Journal of Mathematics . Vol . 10 , 18-22p
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