The Cauchy Problem for Nonlinear Higher Order Partial Differential Equations Using Projected Differential Transform Method

Abstract

This study applies the Projected Differential Transform Method (PDTM) to solve nonlinear higher-order partial differential equations (PDEs). The Projected Differential Transform (PDT) series solutions converge to exact solutions with relative ease. Numerical problems of fourth- and sixth-order nonlinear  hyperbolic equations and nonlinear wave-like equations with variable coefficients are solved to show that PDTM can efficiently provide exact solutions for nonlinear PDEs of higher order with initial conditions. The results demonstrate that the PDTM is exceptionally accurate, efficient, and reliable and that it can be applied to many other types of nonlinear higher-order PDEs. Compared to the Modified Decomposition Method, the Homotopy Analysis Approach, and the Homotopy Perturbation Method, this method significantly reduces numerical computations and outperforms in accuracy.