New predictor-corrector methods of second-order for solving nonlinear equations

In this paper, two predictor-corrector methods are proposed for solving nonlinear equations by combining the fuzzy parameterized method with the exponential iterative method and the regula falsi method. The parameter values are determined by a Gamma-fuzzy number in the iterative procedure. These two methods present attractive features such as being independent of the initial values, or being adaptive for the iterative formulas. They are verified to also be quadratically convergent. Compared with the previously well-known methods, numerical experiments show that new predictor-corrector methods are effective.