|
Document Type |
: |
Thesis |
|
Document Title |
: |
Some new iterative schemes for nonlinear problems طرق تكرارية جديدة لمعادلات غير خطية |
|
Subject |
: |
Faculty of Science |
|
Document Language |
: |
Arabic |
|
Abstract |
: |
One of the most basic and ancient problem of numerical analysis is to find an effective and accurate approximate solution of the nonlinear equation of the form:
f(x)=0.
where f:I⊆C→C is an analytic function in the region including the required x=r (where r is the zero of nonlinear equation).
In general, it is not always possible to obtain the solution of a nonlinear problems by analytical approach. So, it is necessary to adopt the iterative procedure for obtaining the approximate solutions, we have several problems in the real life where the exact solution is not available then we have to satisfy ourselves with approximate solutions. In this way, iterative method fills the gap of exact solution by approximate zero. When we study the iterative methods we look at it is accuracy, order of convergence and how much time will take to get the approximation of the solution. Also, almost all the iterative methods needs the knowledge of one or more initial guesses to obtain the required root of the equation.
In the thesis, we proposed a new King's family of iterative methods. It has advantages it attains optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). Our scheme also fulfill the optimal Kung-Traub conjecture of iterative methods without memory. We also compared our scheme with another iterative methods of the same order of convergence in some real-life problems. We conclude from the obtain results that our methods perform better than the existing.
We also proposed technique has special properties: a two-point method that does not involve any derivatives, has an optimal convergence of fourth-order, and working for multiple roots (m≥2). We have demonstrated the applicability of our methods to six numerical problems. We concluded on the basis of obtained CPU timing, computational order of convergence, and absolute errors between two consecutive iterations for which our methods illustrate better results as compared to earlier studies.
Keywords: King's method; nonlinear equations; optimal iterative methods; multiple roots; Kung-Traub conjecture |
|
Supervisor |
: |
Dr. Ramandeep Behl |
|
Thesis Type |
: |
Master Thesis |
|
Publishing Year |
: |
1444 AH
2023 AD |
|
Co-Supervisor |
: |
Dr. Fouad Othman Mallawi |
|
Added Date |
: |
Thursday, April 27, 2023 |
|
Researchers
| ماجد عالي السلمي | Alsulami, Majed Aali | Researcher | Master | |
|