Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTwo New Methods for Solving Systems of Nonlinear Equations
طريقتان جديدتان لحل جمل المعادلات غير الخطية
3358
6 107
0
(
0
)
Authors
نضال ابراهيم حسن( باحث )
Created by
Shamra Editor
Ask ChatGPT about the research
نقدم في هذا العمل طريقتين عدديتين لإيجاد الحلول العددية لجمل المعادلات غير الخطية. إن الفكرة الأساسية تقوم على مبدأ وجود علاقة بين النهاية الدنيا لدالة و حل جملة المعادلات غير الخطية. الطريقة الأولى تبحث عن الحل العددي وفق متتالية من متجهات البحث المعرفة بدلالة متجه التدرج و مصفوفة هيسيان للدالة F, بينما الطريقة الثانية تعتمد على إنشاء متتالية من متجهات البحث المترافقة. تم إثبات تقارب الطريقتين المقترحتين، و أنهما يقدمان حلولا دقيقة إذا كانت الدالة تربيعية، و ستكون الحلول تقريبية لأجل الدوال فوق التربيعية. تم تنفيذ خوارزميتي الطريقتين المقترحتين باستخدام برنامج Mathemtica النسخة التاسعة. اختبرت فعالية الطريقتين المقترحتين بتطبيقهما لإيجاد الحلول التقريبية لبعض المسائل، و تشير النَتائِج العددية إلى فعالية و دقة الطريقتين بالمقارنة مع بعض الطرائق الأخرى.
In this paper, we present two new methods for finding the numerical solutions of systems of the nonlinear equations. The basic idea depend on founding relationship between minimum of a function and the solution of systems of the nonlinear equations. The first method seeks the numerical solution with a sequence of search directions, which is depended on gradient and Hessian matrix of function, while the second method is based on a sequence of conjugate search directions. The study shows that our two methods are convergent, and they can find exact solutions for quadratic functions, so they can find high accurate solutions for over quadratic functions. The purposed two algorithms are programmed by Mathematica Version9. The approximate solutions of some test problems are given. Comparisons of our results with other methods illustrate the efficiency and highly accurate of our suggested methods.
References used
AMAYA I., J. CRUZ, R. CORREA, Real Roots of Nonlinear Systems of Equations Through a Metaheuristic Algorithm, University Industrial de Santander, No. 170, 2011, pp. 15-23
ARDELEAN, G., The Attraction Basins Of Iterative Methods for Solving Nonlinear Equations, Ph.D. Thesis, Technical University of Cluj-Napoca,North University Center at Baia Mare, Faculty of Sciences, 2012, pp. 1-56
GROSAN C., A. Abraham, T. Norway, Multiple Solutions for a System of Nonlinear Equations, International Journal of Innovative, Computing, Information and Control, Vol. x, No. x, 2008, pp. 1-12
rate research
Read More
In this paper, we described tow parallel algorithms for finding the solution of
symmetric pentadiagonal linear systems of equations of order n . The proposed algorithms
require 2 processors; each of both possesses
N
O n local memor
y.
The first algorithm includes writing the pentadiagonal matrix in the form of product
of tow tridiagonal matrices. We suggested a parallel algorithm for solving tridiagonal
linear systems of equations. The second algorithm consists of decomposition of the
pentadiagonal matrix in a form such that we can carry out the resulting linear systems of
equations by using parallel algorithm. We carried out many numerical experiments to
illustrate the efficiency, speeding up and accuracy for solving symmetric pentadiagonal
linear systems of equations. The numerical experiments showed that the proposed
algorithms were efficient and one of both was much faster in factor of 2 than the other one
for solving the same test problems.
In this Searching scientific, , we introduced three methods for
finding the solution of pentadiagonal linear systems of equations.
In this work, we present programming solutions for some nonlinear partial differential equations, which are the advection equation, the third-order KdV
equations, and a family of Burgers' equations.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
