Document Details

Document Type : Thesis 
Document Title :
Higher-order iterative methods for simple and multiple roots of nonlinear equations
طرق تكرارية عالية الترتيب لجذور بسيطة و متعددة لمعادلات غير خطية
 
Subject : Faculty of Science 
Document Language : Arabic 
Abstract : One of the most basic and earliest problem of numerical analysis concerns with finding efficiency and accurately the approximate solution of the nonlinear equation of the form: f(x) = 0, where f : D ⊆ C → C is an analytic function in the region including the required ∝ (where ∝ is a root of nonlinear equation). Analytic methods for obtaining exact solutions of such problems are almost nonexistence. Therefore, one has to find the approximate solutions by relying on numerical methods which are based on iterative procedures. There are several one-point as well as multi-point iterative methods are available in the literature to solve these equations. Therefore, the construction of iterative methods for solving nonlinear equations is practically important and interesting task, which has attracted the attention of many researchers around the world. Therefore, the main goal and motivation in the suggest and development of new equally competitive methods is to achieve highest computational efficiency with a fixed number of function evaluations per iteration. In our thesis, we have proposed and developed several new families of methods for obtaining simple and multiple roots of nonlinear equations. Furthermore, we intend to suggest an iteration function of sixteenth-order in a general way methods for approximating simple zeros of nonlinear functions and to develop and analyze optimal fourth-order iterative methods for approximating multiple zeros of nonlinear functions. Further, we fully investigated the theoretical and computational properties of the proposed and developed schemes through the main theorem which demonstrates the convergence order and the term of asymptotic error. Computational consequences that the proposed and developed methods are superior than the earlier studies of sixteenth-order in terms of approximated simple roots and optimal fourth-order iterative methods for approximated multiple zeros , terms of asymptotic error, residual errors in the considered functions, variation in two consecutive iterations, etc. 
Supervisor : Dr. Ramandeep Behl 
Thesis Type : Master Thesis 
Publishing Year : 1441 AH
2020 AD 
Co-Supervisor : Dr. Fouad Othman Mallawi 
Added Date : Thursday, May 28, 2020 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
محمد علي محنشيMAHNASHI, Mohammed AliResearcherMaster 

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