scholarly journals An optimal fourth order method for solving nonlinear equations

2020 ◽  
Vol 23 (02) ◽  
pp. 86-97
Author(s):  
M. A. Hafiz ◽  
M. Q. Khirallah
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Method ◽  
Fourth Order Method

scholarly journals Optimal Methods for Finding Simple and Multiple Roots of Nonlinear Equations and their Basins of Attraction

2020 ◽  
Vol 37 (1-2) ◽  
pp. 14-29
Author(s):  
Prem Bahadur Chand
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Multiple Root ◽  
Basins Of Attraction ◽  
Weight Functions ◽  
Multiple Roots ◽  
Order Method ◽  
Numerical Examples ◽  
Fourth Order Method ◽  
Simple And Multiple Roots

In this paper, using the variant of Frontini-Sormani method, some higher order methods for finding the roots (simple and multiple) of nonlinear equations are proposed. In particular, we have constructed an optimal fourth order method and a family of sixth order method for finding a simple root. Further, an optimal fourth order method for finding a multiple root of a nonlinear equation is also proposed. We have used different weight functions to a cubically convergent For ntini-Sormani method for the construction of these methods. The proposed methods are tested on numerical examples and compare the results with some existing methods. Further, we have presented the basins of attraction of these methods to understand their dynamics visually.

scholarly journals Design and Complex Dynamics of Potra–Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 942 ◽  
Author(s):  
Prem B. Chand ◽  
Francisco I. Chicharro ◽  
Neus Garrido ◽  
Pankaj Jain
Keyword(s):  
Nonlinear Equations ◽  
Fourth Order ◽  
Complex Dynamics ◽  
Basins Of Attraction ◽  
Weight Functions ◽  
Order Method ◽  
Eighth Order ◽  
Numerical Examples ◽  
Fourth Order Method ◽  
Cubic Polynomials

In this paper, using the idea of weight functions on the Potra–Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods are tested on some numerical examples, and the results are compared with some known methods of the corresponding order. It is proved that the results obtained from the proposed methods are compatible with other methods. The proposed methods are tested on some problems related to engineering and science. Furthermore, applying these methods on quadratic and cubic polynomials, their stability is analyzed by means of their basins of attraction.

scholarly journals Some Class of Third- and Fourth-Order Iterative Methods for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
J. P. Jaiswal
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Basins Of Attraction ◽  
Order Method ◽  
Third Order ◽  
Numerical Examples ◽  
Multivariate Extension ◽  
New Class ◽  
Fourth Order Method

The object of the present work is to give the new class of third- and fourth-order iterative methods for solving nonlinear equations. Our proposed third-order method includes methods of Weerakoon and Fernando (2000), Homeier (2005), and Chun and Kim (2010) as particular cases. The multivariate extension of some of these methods has been also deliberated. Finally, some numerical examples are given to illustrate the performances of our proposed methods by comparing them with some well existing third- and fourth-order methods. The efficiency of our proposed fourth-order method over some fourth-order methods is also confirmed by basins of attraction.

scholarly journals Attracting Periodic Cycles for an Optimal Fourth-Order Nonlinear Solver

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Mi Young Lee ◽  
Changbum Chun
Keyword(s):  
Periodic Orbit ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Order Method ◽  
Rational Map ◽  
Nonlinear Solver ◽  
Fourth Order Method ◽  
Periodic Cycles

We consider an optimal fourth-order method for solving nonlinear equations and construct polynomials such that the rational map arising from the method applied to these polynomials has an attracting periodic orbit of any prescribed period.

Dynamic Analysis of Prey-Predator Model with Harvesting

2020 ◽  
Vol 5 (5) ◽  
pp. 22-27
Author(s):  
Puskar R. Pokhrel ◽  
Bhabani Lamsal
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Dynamic Analysis ◽  
Fourth Order ◽  
Model Equation ◽  
Order Method ◽  
Eigen Values ◽  
Predator Model ◽  
The Stability ◽  
Fourth Order Method

Employing the Lotka -Voltera (1926) prey-predator model equation, the system is presented with harvesting effort for both species prey and predator. We analyze the stability of the system of ordinary differential equation after calculating the Eigen values of the system. We include the harvesting term for both species in the model equation, and observe the dynamic analysis of prey-predator populations by including the harvesting efforts on the model equation. We also analyze the population dynamic of the system by varying the harvesting efforts on the system. The model equation are solved numerically by applying Runge - Kutta fourth order method.

scholarly journals A fourth order method for finding a simple root of univariate function

2015 ◽  
Vol 34 (2) ◽  
pp. 197-211
Author(s):  
D. Sbibih ◽  
Abdelhafid Serghini ◽  
A. Tijini ◽  
A. Zidna
Keyword(s):  
Iterative Method ◽  
Fourth Order ◽  
Newton’S Method ◽  
Simple Root ◽  
Newton's Method ◽  
Order Method ◽  
Numerical Examples ◽  
Quadratic Interpolation ◽  
Univariate Function ◽  
Fourth Order Method

In this paper, we describe an iterative method for approximating asimple zero $z$ of a real defined function. This method is aessentially based on the idea to extend Newton's method to be theinverse quadratic interpolation. We prove that for a sufficientlysmooth function $f$ in a neighborhood of $z$ the order of theconvergence is quartic. Using Mathematica with its high precisioncompatibility, we present some numerical examples to confirm thetheoretical results and to compare our method with the others givenin the literature.

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