Superlinear bracketing method for solving nonlinear equations

A new method based on Muller’s algorithm for solving nonlinear equations has been developed. The classic Muller’s method is based on an interpolating polynomial built on the last three points of an iterative sequence. Unfortunately, Muller’s method is not globally convergent. In order to ensure the global convergence a bracketing is introduced. The proposed method does not require the use of a derivative of the function and is more rapidly convergent than a classical regula falsi method. The method is good alternative to other bracketing methods.