<p>This work explores an efficient semi-analytical method called the natural decomposition method (NDM) for finding the solution of nonlinear mathematical physics problems under proper initial conditions. The NDM is a hybrid approach that combines the natural transform method (NTM) and the Adomian decomposition method (ADM). The suggested approach provides a succession of approximate analytical solutions that converge rapidly to the exact solution. To demonstrate the efficiency and validity of the suggested method, six illustrative examples are considered. The NDM convergence and solution uniqueness, with their proof, are provided. A graphical appraisal of the approximated and exact solution was implemented. Convergence analysis of the approximations exploiting absolute and relative errors was performed via tables. The NDM results are compared with analytical and numerical solutions existing in the literature. The results reveal that the proposed method is more accurate and reliable than the other methods in the literature. Therefore, the NDM is an efficient tool and has the potential to solve complicated nonlinear problems in a wide range of scientific and engineering applications.</p>