Abstract
In this paper, we mainly study the numerical algorithms for simple root of nonlinear equations based on Newton-Raphson method. Two modified Newton-Raphson methods for solving nonlinear equations are suggested. Both of the methods are free from second derivatives. Numerical examples are made to show the performance of the presented methods, and to compare with other ones. The numerical results illustrate that the proposed methods are more efficient and performs better than Newton-Raphson method.
Highlights
Nonlinear problems is an important direction of research in the field of numerical calculation
To improve the convergence properties, we consider iterative method to find a simple root x * of a nonlinear equation f (x) 0, where f : R R for an open interval is a scalar function and it is sufficiently differentiable in a neighborhood of x *
It is well known that Newton-Raphson method is a basic and important method for solving nonlinear equation [1] using the iterative expression xn 1
Summary
Nonlinear problems is an important direction of research in the field of numerical calculation. We can use iterative methods such as Newton's method (NM), Newton-Raphson method (NRM) or their variants. To improve the convergence properties, we consider iterative method to find a simple root x * of a nonlinear equation f (x) 0 , where f : R R for an open interval is a scalar function and it is sufficiently differentiable in a neighborhood of x *. It is well known that Newton-Raphson method is a basic and important method for solving nonlinear equation [1] using the iterative expression xn 1
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
