Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSpline Method with Three Collocation Parameters for Solving Ninth-Order General Differential Equations Subject to Boundary Conditions
طريقة شرائحية بثلاثة وسطاء تجميع لحل مسائل في المعادلات التفاضلية المعممة من المرتبة التاسعة خاضعة لشروط حدية
2189
0 26
0
(
0
)
Added by
Tishreen University ورقة بحثية
Publication date
2015
fields
Mathematics
and research's language is
العربية
Created by
Shamra Editor
Ask ChatGPT about the research
يتم في هذا العمل استخدام كثيرات حدود شرائحية من الدرجة الحادية عشرة مع ثلاث نقاط تجميع لتطوير طريقة لحساب الحل العددي و مشتقاته حتى المرتبة التاسعة لمسائل القيم الحدية الخطية و غير الخطية في المعادلات التفاضلية المعممة من المرتبة التاسعة. تبين الدراسة أن الطريقة الشرائحية المقترحة عندما طُبِقتْ بثلاث نقاط تجميع لهذه المسائل كانت موجودة و معرفة بشكل وحيد. كما تظهر الدراسة التحليلية للتقارب أن الطريقة المقترحة مستقرة و متناسقة من الرتبة الحادية عشرة و تملك معدل تقارب يزيد عن ستة. كما تم اختبار الطريقة الشرائحية بحل بعض المسائل التطبيقية، إذ تشير المقارنات لنتائجنا مع نتائج عددية لبعض الطرائق المذكورة في مراجع أخرى حديثة إلى أفضلية النتائج التي توصلنا إليها من حيث الاستقرار و الدقة العددية.
In this paper, we use polynomial splines of eleventh degree with three collocation points to develop a method for computing approximations to the solution and its derivatives up to ninth order for general linear and nonlinear ninth-order boundary-value problems (BVPs). The study shows that the spline method with three collocation points when is applied to these problems is existent and unique. We prove that the proposed method if applied to ninth-order BVPs is stable and consistent of order eleven, and it possesses convergence rate greater than six. Finally, some numerical experiments are presented for illustrating the theoretical results and by comparing the results of our method with the other methods, we reveal that the proposed method is better than others.
References used
(ALI J., S. ISLAM, H. KHAN, and Syed Inayat Ali Shah, The Optimal homotopy asymptotic method for the solution of higher-order boundary value problems in finite domains, Abstract and Applied Analysis, Vol. 2012, Article ID 401217, 1-14(2012
Hassan H. Abdel-Halim, Vedat Suat Ertürk, Solutions of Different Types of the linear and Non-linear Higher-Order Boundary Value Problems by Differential Transformation Method, Eur. J. Pure Appl. Math, Vol.2,No 3 (2009), 426-447
Hassan H. Abdel-Halim, Mohamed I. A. Othman and A. M. S. Mahdy, Variational Iteration Method for Solving Twelve Order Boundary Value Problems, Int. Journal of Math. Analysis, Vol. 3, 2009, no. 15, 719 – 730
rate research
Read More
In this paper, a spline collocation method is developed for finding numerical solutions of general linear eighth-order boundary-value problems (BVPs) and nonlinear eighth-order initial value problems (IVPs). The presented collocation method affords t
he spline solution by the polynomial of degree eleventh which satisfies the BVPs and IVPs at three collocation points. The study shows that the spline collocation method when is applied such this problems is existent and unique. Moreover, the purposed method if applied to these systems will be consistent and the global truncation error equal eleventh.
Numerical results are given for four examples to illustrate the implementation and efficiency of the method. Comparisons of the results obtained by the present method with results obtained by the other methods reveal that the present method is very effective and convenient.
In this paper, we introduce a numerical method for solving systems of high-index differential algebraic equations. This method is based on approximating the exact solution by spline polynomial of degree eight with five collocation points to find the
numerical solution in each step. The study shows that the method when applied to linear differential-algebraic systems with index equal one is stable and convergent of order 8, while it is stable and convergent of order 9-u for index equal u .
Numerical experiments for four test examples and comparisons with other available results are given to illustrate the applicability and efficiency of the presented method
In this paper, spline collocation method is considered for solving two forms of problems. The first form is general linear sixth-order boundary-value problem (BVP), and the second form is nonlinear sixth-order initial value problem (IVP). The existen
ce, uniqueness, error estimation and convergence analysis of purpose methods are investigated. The study shows that proposed spline method with three collocation points can find the spline solutions and their derivatives up to sixth-order of the two BVP and IVP, thus is very effective tools in numerically solving such problems. Several examples are given to verify the reliability and efficiency of the proposed method. Comparisons are made to reconfirm the efficiency and accuracy of the suggested techniques.
In this paper: the Daubechies families of wavelets Daubechies
and multi resolution analysis based on Fast Fourier Transform
algorithm (FWT) have been applied to solve some differential
equations with Boundary Value.
In this paper, we present a numerical algorithm for solving linear integro differential Volterra-Friedholm equations by using spline polynomials of degree ninth with six collocation points. The Fredholm-Volterra equation is converted into a system of
first-order linear differential equations, which is solved by applying polynomials and their derivatives with collocation points. The convergence of the proposed method is demonstrated when it is applied to above problem. To test the effectiveness and accuracy of this method, two test problems were resolved where comparisons could be used with other results taken from recent references to the high resolution provided by spline approximations.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
