The main focus of the paper aims to illustrate application of the Reduced Differential Transform Method (RDTM). The technique is utilized directly excluding the use of bilinear forms, Wronskian functions, and the inverse scattering technique. A significant feature of the RDTM is it optimize the convergence to the analytical solution as the series expansion order increases. In this research, the method is applied to solve the nonlinear (1 + 1)-dimensional Kaup system and the Sawada-Kotera-Ito seventh-order KdV equation, considering initial conditions that include the arbitrary constants. Numerical results produced from RDTM is examined with exact solutions, with fixed arbitrary constants and the output presented in table from and graphical representation. The computational efficiency of RDTM is illuminated by its ability to produce high-accuracy solutions with minimal terms in the series expansion. Error analysis confirms the method’s efficiency, with results closely meets with exact solutions even for complex nonlinear terms. Furthermore, the simplicity of implementation i.e. avoiding restrictive assumptions or transformations, makes RDTM more useful practically. These attributes position RDTM as a powerful alternative to conventional analytical and numerical techniques for nonlinear PDEs.