Solution of Non-linear Equations using Bisection Method by New Technical Method | ||||
| المجلة العربية للعلوم التربوية والنفسية | ||||
| Article 13, Volume 6, Issue 26, February 2022, Page 261-274 PDF (662.01 K) | ||||
| Document Type: المقالة الأصلية | ||||
| DOI: 10.21608/jasep.2022.216291 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| Subhi Abdalazim Aljily Osman1; Abdel Radi Abdel Rahman Abdel Gadir Abdel Rahman2; Adam Osman Ali Mohammed3; Abualez Alamin Ahmed Ali4 | ||||
| 1Department of Mathematics , Faculty of Computer Science and Information Technology, University of ALBUTANA, Rufaa Sudan | ||||
| 2GadirDepartment of Mathematics, Faculty of Education, Omdurman Islamic University, Omdurman, Sudan | ||||
| 3Department of Mathematics, Faculty of Engineering, Sennar University, Sennar, Sudan | ||||
| 4Department of Mathematics, Faculty of Education, University of Holly Quran and Tassel of Science, Rufaa, Sudan | ||||
| Abstract | ||||
| Numerical approximation of the root-finding problem its important tool for process involves finding a root, or solution of nonlinear equation of the form , for a given function f. A root of this equation is also called a zero of the function When we implementing the method on a computer we need to consider the effects of round-off error. For example the computation of the midpoint of the interval should be found from the equation . The Bisection method is used to determine to any specified accuracy that your computer will permit a solution to on an interval , provided that f is continuous on the interval and that are of opposite sign. Although the method will work for the case when more than one root is contained in the interval , we assume for simplicity of our discussion that the root in this interval is unique. the method stops if one of the midpoints happens to coincide with the root. It also stops when the length of the search interval is less than some prescribed tolerance. The having method is characterized by the fact that it always includes convergence of the individual islands. It is also characterized by the case of calculating errors, but one of its disadvantages is that it is slow to converge to reach the solution. To compare with the a new technical method of the solution . We followed applied numerical method using a new technical method in computer and we found that the new technical method of solution is much faster and more accurate. | ||||
| Keywords | ||||
| Solution; Non-linear Equations; Bisection Method; New Technical Method | ||||
| References | ||||
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[1] ChamanLalSabharwal, Blended Root Finding Algorithm Outperforms Bisection and RegulaFalsi Algorithms, Published: 16 November 2019 [2] AlojzSuhadolnik, Combined bracketing methods for solving nonlinear equations, Volume 25, Issue 11, November 2012 [3] J.-C. Yakoubsohn, Numerical analysis of a bisection-exclusion method to find zeros of univariate analytic functions, , 21 June 2005 [4] M. Embree, Rice University, NUMERICAL ANALYSIS , 29 November 2009. [5] Kendall E. Atkinson , John Wiley & Sons, AN INTRODUCTION TO NUMERICAL ANALYSIS , Second Edition, 1978 [6] SomkidIntep, A Review of Bracketing Methods for Finding Zeros of Nonlinear Functions, Applied Mathematical Sciences,Vol. 12, 2018 [7] S.S .SASTRY. Introductory methods of numerical analysis PHI Learning private limited New Delhi-110001, fifth Edition 2012. [8] Richard L. Burden, J. Douglas Faires, Numerical Analysis, Ninth Edition, 2011 [9] Steven T. Karris, Numerical Analysis, Second Edition, 2004
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