“Comparative Performance Study of Fourier-Based Differential Transformation and Spectral Techniques for Differential Equations.”

Abstract

This study provides a comparative investigation of the Fourier-based Differential Transform Method (Fourier–DTM) and classical spectral techniques for solving nonlinear differential equations defined over periodic domains. To assess the performance of the Fourier–DTM, it is systematically compared with Chebyshev spectral methods and wavelet-based approaches in terms of accuracy and computational efficiency. The numerical findings demonstrate that the Fourier–DTM exhibits superior convergence characteristics, enhanced numerical stability, and reduced computational effort. The effectiveness of the proposed approach is illustrated through several benchmark problems, including the heat equation, wave equations with periodic forcing, and the Fisher equation.