On integral invariants of ruled surface generated by the Darboux frame of the transversal intersection timelike curve of two timelike surfaces in Lorentz-Minkowski 3-space

In this paper, we propose a new two-parameter class of iterative methods to solve a nonlinear equation. It is proved that any method in this class is cubically convergent if and only if the parameters sum up to one. Some of the existing third-order methods, by suitable selection of parameters, can be put in this class. Every iteration of the class requires an evaluation of the function, three of the first derivative, and none of the second derivative. Hence, its efficiency index is 31/4 = 1.316 that is worse than all other cubically convergent methods considered. However, numerical experiments show that a special method in our class is comparable to those in terms of iterations number.