<p>Two effective iterative methods are developed in this paper for solving nonlinear initial value problems, including the well-known Riccati differential equations. The proposed methods combine quasilinearization and the Picard approach, in which quasilinearization is used to transform a given nonlinear equation into a sequence of linearized equations, and the Picard approach is subsequently applied to obtain approximate solutions of these linear problems. The proposed methods are referred to as the quasi-linearized Picard iteration method (QPIM) and piecewise QPIM. The main advantage of the proposed schemes is their ability to provide highly accurate solutions in just a few iterations. In addition, the piecewise QPIM scheme is uniform, enhances the convergence region of the approximate solution, and provides an acceptable approximate solution, even over large intervals. Several numerical examples are presented to illustrate the applicability and robustness of the proposed schemes. The numerical results reflect the superiority of the proposed approaches over existing methods.</p>