An improved memory method for the solution of a nonlinear equation

A new method, the improved memory method, for the solution of a nonlinear equation is introduced. This method is compared with several widely used solution methods by solving 15 test problems from different chemical engineering application areas. It is shown that the proposed method requires the smallest number of function (or derivative) evaluations to achieve the solution. A new algorithm for stopping the iterations is introduced. This algorithm stops the iterations when the true error is reduced for the first time below the desired error tolerance.