Efficient Solving of Nonlinear ODEs: Daftardar-Jafari Method vs Differential Transform Method

Abstract

This study explores the Daftardar-Jafari Method (DJM) for solving linear and nonlinear ordinary differential equation systems (ODEs). Unlike traditional perturbation methods, DJM does not rely on small parameters, making it highly effective for strongly nonlinear problems. The method constructs a rapidly converging iterative sequence, yielding accurate analytical or approximate solutions with reduced computational costs. We applied DJM to a range of benchmark problems and compared the results with those obtained using the differential transform method (DTM). The DJM provided significantly higher accuracy, demonstrating its superior performance in terms of convergence and computational efficiency. The numerical results, computed using Maple software, reinforce the practical advantages of DJM for solving complex systems of ODEs. In conclusion, DJM is an effective and efficient tool for solving a broad class of ordinary differential equation systems, outperforming traditional methods like the differential transform method in terms of accuracy and reliability.