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Article
Compare Between Least Square Method and Petrov-Galerkin Method for Solving the First Order Linear Ordinary Delay Differential Equations

Author: Sinan Hatif Abd Almjeed
Journal: Journal of Education for Pure Science مجلة التربية للعلوم الصرفة ISSN: 20736592 Year: 2017 Volume: 7 Issue: 4 Pages: 16-27
Publisher: Thi-Qar University جامعة ذي قار

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Abstract

Abstract:The problem of find approximate solution for the first order linear ordinary delay differentialequations by using two of the special cases of the weighted residual method which are the leastsquares method and Petrov-Galerkin method with compare between these methods for which the bestapproximate solution near to the exact solution, also numerical applications are considered in thiswork.


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

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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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