A new approach for solving nonlinear equations

In this paper, we describe and analyze an efficient method to find the roots of a general one variable function f:\mathbb{R}\rightarrow \mathbb{R}. The proposed method is based on partitioning an interval (that probably contains root(s) of f) into subintervals. From this point of view, we name this method a finite element approach for root finding. Also the convergence analysis of the presented method is presented. The new approach can be generalized to estimate the roots of the multivariable functions in higher dimensions. Also it is capable to find all of the roots of the function on a determined interval. Finally, numerical examples are given to illustrate the effectiveness of the new method.

Keywords:

Nonlinear function , finite element approach , piecewise Lagrange interpolation