Validation of SAWI Transformation for Nonlinear Differential Equations Using Fourth‑Order Runge‑Kutta

Abstract

This paper investigates the method of Shifted and Weighted Integral (SAWI) transformation for solving a nonlinear system of ordinary differential equations (ODEs) with quadratic nonlinearity. The approach semi-analytical solution is validated by comparison with the classical fourth-order Runge-Kutta (RK4) method. Numerical results show that the absolute errors demonstrating strong agreement between both approaches. The SAWI technique transforms the connected nonlinear system into a set of differential equations in the sigma-domain. The agreement between the two approaches for the quadratically nonlinear system confirms the reliability and efficiency of the SAWI transformation as a semi-analytical technique, providing analytically valid and computationally efficient analysis of such systems.