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Article
Using Bernoulli Equation to Solve Burger's Equation
استخدام معادلة برنو لي لحل معادلة بيركر

Authors: Muna Saleh منى صالح --- Saad N. AL-Azawi سعد ناجي العزاوي
Journal: Baghdad Science Journal مجلة بغداد للعلوم ISSN: 20788665 24117986 Year: 2014 Volume: 11 Issue: 2 عدد خاص بالمؤتمر النسوي الثاني Pages: 202-206

Abstract

In this paper we find the exact solution of Burger's equation after reducing it to Bernoulli equation. We compare this solution with that given by Kaya where he used Adomian decomposition method, the solution given by chakrone where he used the Variation iteration method (VIM)and the solution given by Eq(5)in the paper of M. Javidi. We notice that our solution is better than their solutions.

حصلنا من بحثنا هذا على الحل المضبوط (Exact) لمعادلة بيركر بعد تحويلها إلى معادلة برنو لي وتمت مقارنة هذا الحل مع حل "Kaya"الذي استخدم طريقة تجزئة ادومين وحل "Chakrone" الذي أستخدم طريقة التغاير المتكرر وحل "Javidi" المعطى بالعلاقة (5)وتبين ان حلنا هذا افضل من حلولهم للبساطه الصيغة

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

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.

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Article
Numerical Solution for Fractional Order Space-Time Burger's Equation Using Legendre Wavelet - Chebyshev Wavelet Spectral Collocation Method

Authors: Osama H. Mohammed --- Mohammed G. S. AL-Safi --- Ahmed Ayyoub Yousif
Journal: Al-Nahrain Journal of Science مجلة النهرين للعلوم ISSN: (print)26635453,(online)26635461 Year: 2018 Volume: 21 Issue: 1 Pages: 121-127
Publisher: Al-Nahrain University جامعة النهرين

Abstract

In this article, a Legendre wavelet- Chebyshev wavelet spectral collocation method is proposed for solving fractional order space-time Burger's equation with the Legendre wavelet and Chebyshev wavelet operational matrices of fractional derivatives. The fractional derivative is described in the Caputo sense. The proposed method is based on Legendre wavelet-Chebyshev wavelet for space and time variables respectively. This method will reduc the problem under consideration to the solution of nonlinear algebraic equations. In order to confirm the efficiency of the proposed method, two numerical examples are implemented and comparing the numerical solution with the exact one, as well as, of other methods in given literatures, we demonstrate the high accuracy and efficiency of the proposed method.

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Article
Approximation of Burger's Equation Using Sextic B-Spline Galerkin Scheme with Quintic Weight Function

Author: Akeel Abdulwahid Qasim
Journal: Journal of University of Babylon مجلة جامعة بابل ISSN: 19920652 23128135 Year: 2018 Volume: 26 Issue: 8 Pages: 19-28
Publisher: Babylon University جامعة بابل

Abstract

In this study Weproduce new numerical scheme which rely on sextic B-spline Galerkin method takes with quintic B-spline as a weight function, for solving the Burger's equation, contrasted with exact solution can be done and then we find out a linear stability analysis which is erect on a Fourier (Von Neumann) method.

في هذه الدراسة قمنا باستخدام نظام عددي جديد لحساب الحل التقريبي لمعادلة (بيرغر) وذلك باعتماد دالة وزن تقل بقدار واحد عن درجة دالة الـ(سبلاين كالركن من النوع B) حيث كانت دالة الـ (كالركن) من الدرجة السادسة ودالة الوزن من الدرجة الخامسة. وبعد مقارنة النتائج التي حصلنا عليها مع الحل التحليلي لمعادلة (بيرغر) وجدنا ان هذا الأسلوب كان جيداً و غير شرطي الاستقرار من خلال استخدامنا لطريقة فورير(فان نيومن)لدراسة استقرارالاسلوب المقدم.

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