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

Volume: 10    Issue: 2

Year of Publication: 2025

Pages: 48-51

Authors: Dr. George Albert Toma

DOI: https://doi.org/10.5281/zenodo.15575487

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Abstract

This study explores the Daftardar-Jafari Method (DJM) for solving linear and nonlinear higher-order ordinary differential equations (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 Homotopy Perturbation Method (HPM). 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 higher-order ordinary differential equations. In conclusion, DJM is an effective and efficient tool for solving a broad class of higher-order ordinary differential equations, outperforming traditional methods in terms of accuracy and reliability.

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Keywords

Linear and nonlinear equation, higher-order ordinary differential equation, Daftardar-Jafari Method, Exact and approximate solution.