The quasi-static (QS) method had been devised for efficient analyses of reactor transients, and two different approaches are widely implemented, which are namely Improved Quasi-Static Method (IQM) and Predictor-Corrector Quasi-Static Method (PCQM). Conventionally, both methods regard the shape to be static while deducing the variation of the amplitude. In this paper, the formulation of standard IQM and PCQM methods based on a multi-group neutron diffusion equation is presented along with a description for implementing such methods to feedback-encompassed nonlinear transient calculation. The idea of relaxation in the quasi-static treatment of the shape through polynomial interpolation is proposed, and comparison among the ramifications of having different conjectures, e.g., static, linear, and quadratic relaxation, has been made based on a thermal-hydraulics-coupled one-dimensional two-group reactor representing the pressurized water reactor. It is found that performance of both IQM and PCQM could be clearly improved with polynomial relaxations even for strongly non-linear reactor problems. (C) 2021 Elsevier Ltd. All rights reserved.