Higher order Jarratt-like iterations for solving systems of nonlinear equations

2021 ◽  
Vol 395 ◽  
pp. 125849
Author(s):  
T. Zhanlav ◽  
Kh. Otgondorj
2006 ◽  
Vol 136 (6) ◽  
pp. 1287-1301
Author(s):  
Nalini Joshi ◽  
Andrew Pickering

Towards the end of the nineteenth century, Halphen studied a remarkable sequence of higher-order linear equations with doubly periodic coefficients, generalizations of a certain Lamé equation, having the property that quotients of solutions are single valued. Here we consider further generalizations where, instead of the Weierstrass ℘-function, the coefficients depend on the first Painlevé transcendent. Using these equations, we obtain new higher-order systems of nonlinear equations having the Painlevé property. We also give new results on the interpretation of the Painlevé tests with regard to the representations of solutions, general and particular, afforded by various branches, and to understanding the corresponding pattern of compatibility conditions.


2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Diyashvir K. R. Babajee ◽  
Alicia Cordero ◽  
Fazlollah Soleymani ◽  
Juan R. Torregrosa

This paper focuses on solving systems of nonlinear equations numerically. We propose an efficient iterative scheme including two steps and fourth order of convergence. The proposed method does not require the evaluation of second or higher order Frechet derivatives per iteration to proceed and reach fourth order of convergence. Finally, numerical results illustrate the efficiency of the method.


Sign in / Sign up

Export Citation Format

Share Document