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Article
A Numerical solution of Transport Problems

Author: Taghreed Abdul Kareem
Journal: Misan Journal of Acodemic Studies مجلة ميسان للدراسات الاكاديمية ISSN: 1994697X Year: 2016 Volume: 15 Issue: 29 Pages: 99-112
Publisher: Misan University جامعة ميسان

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Abstract

Abstract: We apply the variational iteration method for solving the transport problems. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The composition is presented between variational iteration method and Adomian Decomposition Method(ADM) and we found that the proposed technique solves this type of problems without using Adomian’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method and the result accuatte than ADM .several examples are given to verify the reliability and efficiency of the method


Article
Solution of Differential-Algebraic Equations(DAEs) by Variational Iteration Method

Author: Taghreed Abdul-Kareem Hatim تغريد عبد الكريم
Journal: Misan Journal of Acodemic Studies مجلة ميسان للدراسات الاكاديمية ISSN: 1994697X Year: 2014 Volume: 13 Issue: 24 Pages: 49-59-E
Publisher: Misan University جامعة ميسان

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Abstract

In this paper, we use variational iteration method (VIM) to handle the differential-algebraic equations(DAEs) systems. The results reveal that the variational iteration method (VIM) is more efficient than the ADM and it is very effective, convenient and quite accurate to systems of linear partial differential equations. It is predicted that VIM can be found widely applicable in engineering.


Article
Approximate Solution of Coupled Burger’s Equation and Advection Diffusion Equation

Authors: A. M. Ayal --- A. N. Alfalah --- M.A. Aljaboor
Journal: Misan Journal of Acodemic Studies مجلة ميسان للدراسات الاكاديمية ISSN: 1994697X Year: 2017 Volume: 16 Issue: 31 Pages: 31-43
Publisher: Misan University جامعة ميسان

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Abstract

AbstractThis paper is devoted to find the approximate solution of the coupled Burgers equation and advection diffusion equation by the Variational Iteration Method (VIM). This method provides a sequence of functions which converges to the exact solution of the system. It has been shown that the (VIM) is quite efficient and suitable for finding the approximate solution of this couple of PDE.


Article
Variational Iteration Method for solving Two-Dimensional Reaction-Diffusion Brusselator System
طريقة التغايرالتكرارية لحل Two-Dimensional Reaction-Diffusion Brusselator System ذات البعدين

Author: T. A. K. Hattim تغريد عبد الكريم حاتم
Journal: Journal of Basrah Researches (Sciences) مجلة ابحاث البصرة ( العلميات) ISSN: 18172695 Year: 2013 Volume: 39 Issue: 4A Pages: 67-80
Publisher: Basrah University جامعة البصرة

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Abstract

This paper proposes the investigation of the variational iteration method to find the solutions for Two-dimensional Reaction-Diffusion Brusselator System . Analytic solutions of the linear partial differential equations with initial data are obtained. It has been shown that the method is quite efficient and is practically well suited for use in these problems. Moreover, a necessary and sufficient condition for convergence is given. Numerical test is investigated to illustrate the pertinent features of the proposed algorithm.

في هذا البحث اقترحنا استعمال طريقة التغايرالتكرارية Two-Dimensional Reaction-Diffusion Brusselator System ذات البعدين . تم الحصول على الحل التحليلي باستعمال هذه الطريقة لهذا النوع من المعادلات التفاضلية الجزئية مع شروطها الابتدائية، حيث بينت الحلول التي حصلنا عليها دقة الطريقة وملاءمتها لحل هذه المسالة. كما تم اعطاء الشرط الضروري للتقارب. ايضا تم تقديم مثال توضيحي لبيان عمل الطريقة.


Article
Variational Iteration Method for Solving Multi-Fractional Integro Differential Equations
الطريقة التغايرية التكرارية لحل المعادلات التفاضلية-التكاملية ذات الرتب الكسورية المتعددة

Author: Omar I. Khaleel عمر اسماعيل خليل
Journal: Iraqi Journal of Science المجلة العراقية للعلوم ISSN: 00672904/23121637 Year: 2014 Volume: 55 Issue: 3A Pages: 1086-1094
Publisher: Baghdad University جامعة بغداد

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Abstract

In this paper, we present an approximate method for solving integro-differential equations of multi-fractional order by using the variational iteration method. First, we derive the variational iteration formula related to the considered problem, then prove its convergence to the exact solution. Also we give some illustrative examples of linear and nonlinear equations.

في هذا البحث، تم تقديم طريقة تقريبية لحل المعادلات التفاضلية التكاملية ذات الرتب الكسورية المتعددة بأستخدام الطريقة التغايرية التكرارية. لقد تم اشتقاق الصيغة التكرارية لحل المسألة المقترحة ومن ثم برهان تقارب متتابعة الحلول الى الحل المضبوط مع إعطاء بعض الامثلة التوضيحية الخطية وغير الخطية لحل هكذا نوع من المعادلات.


Article
Numerical Solution of a Reaction-Diffusion System with Fast Reversible Reaction by Using Adomian’s Decomposition Method and He’s Variational Iteration Method

Authors: Ann J. Al-Sawoor --- Mohammed O. Al-Amr
Journal: AL-Rafidain Journal of Computer Sciences and Mathematics مجلة الرافدين لعلوم الحاسوب والرياضيات ISSN: 18154816 Year: 2012 Volume: 9 Issue: 2 Pages: 243-257
Publisher: Mosul University جامعة الموصل

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Abstract

In this paper, the approximate solution of a reaction-diffusion system with fast reversible reaction is obtained by using Adomian decomposition method (ADM) and variational iteration method (VIM) which are two powerful methods that were recently developed. The VIM requires the evaluation of the Lagrange multiplier, whereas ADM requires the evaluation of the Adomian polynomials. The behavior of the approximate solutions and the effects of different values of are shown graphically.

في هذا البحث، تم إيجاد الحل التقريبي لنظام التفاعل-الانتشار مع تفاعل عكسي سريع باستخدام طريقتين من الطرق الفعالة التي تم تطويرها مؤخراً وهما طريقة تحليل ادومين (ADM) وطريقة التكرار المتغاير (VIM). إن طريقة التكرار المتغاير تتطلب إيجاد مضروب لاكرانج، بينما طريقة تحليل ادومين تتطلب إيجاد متعددات حدود ادومين. كما تم توضيح سلوك الحل التقريبي والتأثيرات لقيم مختلفة لـ عن طريق الرسم.


Article
Application of Local Fractional Variational Iteration Method for Solving Fredholm integral equations Involving Local Fractional Operators

Authors: Hassan Kamil Jassim --- Hussein Khashan Kadhim
Journal: Journal of Univesity of Thi-Qar مجلة جامعة ذي قار العلمية ISSN: 66291818 Year: 2016 Volume: 11 Issue: 1 Pages: 1-7
Publisher: Thi-Qar University جامعة ذي قار

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Abstract

In this paper, the local fractional variational iteration method (LFVIM) is used for solving linear and nonlinear Fredholm integral equations of the second kind within local fractional derivative operators. To illustrate the ability and simplicity of the method, some examples are provided. The results reveal that the proposed method is very effective and simple and it leads to the exact solution

في هذا البحث طريقة التغاير التكراريه الكسريه المحليه استخدمت لحل المعادلات التكاملية الخطية وغير الخطية نوع فردهلم من الصنف الثاني ضمن المؤثرات التفاضلية الكسريه المحليه. لتوضيح قدرة وبساطة الطريقة، قدمت بعض الأمثلة. بينت النتائج أن الطريقة المقترحة هي فعالة جدا وبسيطة وتؤدي إلى الحل الدقيق


Article
A New Efficient Method for solving Helmholtz and Coupled Helmholtz Equations Involving Local Fractional Operators

Authors: Hassan Kamil Jassim --- Hasan Ali Naser --- Alaa Kleef Jiheel
Journal: JOURNAL OF THI-QAR SCIENCE مجلة علوم ذي قار ISSN: 19918690 Year: 2018 Volume: 6 Issue: 4 Pages: 153-157
Publisher: Thi-Qar University جامعة ذي قار

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Abstract

In this manuscript, we apply a new technique, namely local fractional Laplace variational iteration method (LFVITM) on Helmholtz and coupled Helmholtz equations to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators (LFDOs). This method is the combined of the local fractional Laplace transform (LFLT) and variational iteration method (VIM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.


Article
Variational Iteration Method for Solving Boundary Value Problems of Fractional Order

Authors: Fadhel S.Fadhel --- Saif Al-Deen M.Jameel
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2019 Volume: 00 Issue: 2 Pages: 59-64
Publisher: Al-Nahrain University جامعة النهرين

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Abstract

This paper presents an approximate solution of ordinary boundary value problems using the variational iteration method. The fractional derivatives are described in the Caputo sense, because it allows traditional initial and boundary conditions to be included in the formulation of the problem. The solutions of proposed fractional equations are calculated in the form of convergent series with easily computable components. Also, we construct the variational iteration formula and its convergence to the exact solution for solving system of fractional order differential equations. Some examples are solved as an illustration to the method, in order to show the accuracy of the method and comparison with results the exact solution for the given test problems, which are given for comparison purpose.


Article
Analytical Solutions of the One-Dimensional Volterra Integro-Differential Equations within Local Fractional Derivative

Authors: Hassan Kamil Jassim --- Ammar Ali Neamah
Journal: Journal of Kufa for Mathematics and Computer مجلة الكوفة للرياضيات والحاسوب ISSN: 11712076 Year: 2017 Volume: 4 Issue: 1 Pages: 46-50
Publisher: University of Kufa جامعة الكوفة

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Abstract

The one-dimensional Volterra Integro-Differential Equations of the second kind associated with local fractional derivative operators are investigated. Analytical solutions are obtained by using the local fractional variational Iteration method (LFVIM). The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

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