A new method for rooting nonlinear equations based on the Bisection method

Abstract

Finding the roots of nonlinear equations has many applications in various sciences, especially engineering, and various methods have been proposed for this purpose. However, almost all these methods have some shortcoming. This paper presents a new method, where we consider the desired function to find the root(s) of the absolute value, so the root(s) (if any) is the absolute minimum. Using Monte Carlo method, we divide the desired distance into smaller parts. In each section where the slope of the function changes, we use the Bisection method to find the root. It largely covers the limitations of previous methods. The most important advantage of this method over the Bisection method is that it finds all the roots of the equation. • Solve the problem of the bisection method in roots tangent to the x-axis. • Separation of Root(s) that crossed and Root(s) that are tangent to the x-axis.

Keywords

• Improved Bisection method based on slope (IBMS)