Effectiveness of the Daftardar-Jafari Method in Solving Higher-Order Ordinary Differential Equations: A Numerical Study

This study explores the Daftardar-Jafari Method (DJM) for solving linear and nonlinear higher-orderordinary differential equations (ODEs). Unlike traditional perturbation methods, DJM does not rely on smallparameters, making it highly effective for strongly nonlinear problems. The method constructs a rapidlyconverging iterative sequence, yielding accurate analytical or approximate solutions with reduced computationalcosts. We applied DJM to a range of benchmark problems and compared the results with those obtained using theHomotopy Perturbation Method (HPM). The DJM provided significantly higher accuracy, demonstrating itssuperior performance in terms of convergence and computational efficiency. The numerical results, computedusing Maple software, reinforce the practical advantages of DJM for solving complex higher-order ordinarydifferential equations. In conclusion, DJM is an effective and efficient tool for solving a broad class of higherorder ordinary differential equations, outperforming traditional methods in terms of accuracy and reliability.