A new smoothing newton-type two-step algorithm to solve non-lipschitz absolute value equations of the form <inline-formula><tex-math id="M1">$ Ax + B|x|^p = b $</tex-math></inline-formula>

Due to their connection to linear complementarity problems, which affect various fields such as management science, operations research, and engineering, absolute value equations (AVE) are being extensively studied. This work concentrates on the solution of the system of Non-Lipschitz Absolute Value Equations (NAVE), which is one of the recent generations of AVE. We initially modify the existing smoothing techniques for NAVE, which are utilized to convert it into a set of smooth equations with adjustable parameters. Subsequently, Traub's method-based two-step iteration methods are developed by including the suggested smoothing techniques to address the smoothed form of AVE. The numerical experiments are conducted on both widely known and randomly created test problems, followed by an analysis of the findings. Finally, the efficiency of the proposed methods is displayed by comparing them with each other.