A semi-analytical iterative method for solving nonlinear thin film flow problems
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Publication Date
Sat Jul 01 2017
Journal Name
Journal Of King Saud University - Science
(16)
Publication Date
Tue Jan 02 2018
Journal Name
Arab Journal Of Basic And Applied Sciences
(16)
Publication Date
Sat Dec 01 2018
Journal Name
Ain Shams Engineering Journal
(6)
Publication Date
Thu Oct 01 2020
Journal Name
Alexandria Engineering Journal
(5)
Publication Date
Thu Oct 01 2020
Journal Name
Alexandria Engineering Journal
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(5)
Publication Date
Sat Oct 01 2016
Journal Name
International Journal Of Pure And Apllied Mathematics
(10)
Publication Date
Sun Dec 07 2014
Journal Name
Baghdad Science Journal
New Iterative Method for Solving Nonlinear Equations
Nonlinear equation
convergence
three step method
The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.
Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
Three Weighted Residuals Methods for Solving the Nonlinear Thin Film Flow Problem
Abstract<p>In this paper, the methods of weighted residuals: Collocation Method (CM), Least Squares Method (LSM) and Galerkin Method (GM) are used to solve the thin film flow (TFF) equation. The weighted residual methods were implemented to get an approximate solution to the TFF equation. The accuracy of the obtained results is checked by calculating the maximum error remainder functions (MER). Moreover, the outcomes were examined in comparison with the 4<sup>th</sup>-order Runge-Kutta method (RK4) and good agreements have been achieved. All the evaluations have been successfully implemented by using the computer system Mathematica®10.</p>
(1)
Publication Date
Sun Jul 01 2018
Journal Name
Computers & Mathematics With Applications
(19)
Publication Date
Thu Oct 20 2022
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Iterative Method for Solving a Nonlinear Fourth Order Integro-Differential Equation
This study presents the execution of an iterative technique suggested by Temimi and Ansari (TA) method to approximate solutions to a boundary value problem of a 4th-order nonlinear integro-differential equation (4th-ONIDE) of the type Kirchhoff which appears in the study of transverse vibration of hinged shafts. This problem is difficult to solve because there is a non-linear term under the integral sign, however, a number of authors have suggested iterative methods for solving this type of equation. The solution is obtained as a series that merges with the exact solution. Two examples are solved by TA method, the results showed that the proposed technique was effective, accurate, and reliable. Also, for greater reliability, the approxim
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