Numerical simulation of multiple roots of van der Waals and CSTR problems with a derivative-free technique

In this paper, a derivative-free one-point iterative technique is proposed, with memory for finding multiple roots of practical problems, such as van der Waals and continuous stirred tank reactor problems, whose multiplicity is unknown in the literature. The new technique has an order of convergence of 1.84 and requires two function evaluations. It can be used as a seed to produce higher-order methods with similar properties, and it increases the efficiency of a similar procedure without memory due to Schröder. After studying its order of convergence, its stability is checked by applying it to the considered problems and comparing with the technique of the same nature for finding multiple roots. The geometrical behavior of the numerical results of the techniques is also studied.