An efficient family of Steffensen‐type methods with memory for solving systems of nonlinear equations

2021 ◽  
Author(s):  
Mona Narang ◽  
Saurabh Bhatia ◽  
Vinay Kanwar
Keyword(s):  
Nonlinear Equations ◽  
Systems Of Nonlinear Equations ◽  
With Memory

scholarly journals An Efficient Derivative Free One-Point Method with Memory for Solving Nonlinear Equations

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 604 ◽  
Author(s):  
Janak Raj Sharma ◽  
Sunil Kumar ◽  
Clemente Cesarano
Keyword(s):  
Nonlinear Equations ◽  
Efficiency Index ◽  
Point Method ◽  
Function Evaluation ◽  
Systems Of Nonlinear Equations ◽  
Academic Problems ◽  
Similar Nature ◽  
Newton's Iteration ◽  
Derivative Free ◽  
With Memory

We propose a derivative free one-point method with memory of order 1.84 for solving nonlinear equations. The formula requires only one function evaluation and, therefore, the efficiency index is also 1.84. The methodology is carried out by approximating the derivative in Newton’s iteration using a rational linear function. Unlike the existing methods of a similar nature, the scheme of the new method is easy to remember and can also be implemented for systems of nonlinear equations. The applicability of the method is demonstrated on some practical as well as academic problems of a scalar and multi-dimensional nature. In addition, to check the efficacy of the new technique, a comparison of its performance with the existing techniques of the same order is also provided.

scholarly journals Iterative Methods with Memory for Solving Systems of Nonlinear Equations Using a Second Order Approximation

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1069 ◽  
Author(s):  
Alicia Cordero ◽  
Javier G. Maimó ◽  
Juan R. Torregrosa ◽  
María P. Vassileva
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Order Approximation ◽  
Multidimensional Case ◽  
Systems Of Nonlinear Equations ◽  
Simple Method ◽  
The Right ◽  
Interpolation Polynomials ◽  
With Memory

Iterative methods for solving nonlinear equations are said to have memory when the calculation of the next iterate requires the use of more than one previous iteration. Methods with memory usually have a very stable behavior in the sense of the wideness of the set of convergent initial estimations. With the right choice of parameters, iterative methods without memory can increase their order of convergence significantly, becoming schemes with memory. In this work, starting from a simple method without memory, we increase its order of convergence without adding new functional evaluations by approximating the accelerating parameter with Newton interpolation polynomials of degree one and two. Using this technique in the multidimensional case, we extend the proposed method to systems of nonlinear equations. Numerical tests are presented to verify the theoretical results and a study of the dynamics of the method is applied to different problems to show its stability.

scholarly journals A Hybrid Approach for Solving Systems of Nonlinear Equations Using Harris Hawks Optimization and Newton’s Method

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Rami Sihwail ◽  
Obadah Said Solaiman ◽  
Khairuddin Omar ◽  
Khairul Akram Zainol Ariffin ◽  
Mohammed Alswaitti ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Hybrid Approach ◽  
Systems Of Nonlinear Equations
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