Comparative Analysis of the Differential Transform Method and Generalized Fibonacci Collocation Method for Solving Differential Equations

Authors

  • Maha Abdalla Abdou Department of Mathematics, Faculty of Education, International University of Islamic and Linguistic Sciences Postgraduate Studies
  • Amany Saad Mohamed Department of Mathematics, Faculty of Science, Helwan University

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6734

Keywords:

Differential transform method, Generalized Fibonacci polynomials, Collocation method

Abstract

This study investigates two ways of discussing the solution of linear, mixed, and special nonlinear models of second-order differential equations: the differential transform method and the generalized Fibonacci collocation method. The differential transform method uses a step-by-step approach to convert differential equations and their conditions into power series, giving an exact or highly accurate solution. On the other hand, the generalized Fibonacci collocation method transforms the problem into a system of equations with unknown coefficients, which are determined by solving this system using matrix operations. It yields a numerical solution. We discuss convergence and error bounds of generalized Fibonacci polynomials in detail. This study
evaluates the solutions of four different problems, focusing on their reliability and accuracy. This comparison shows that our algorithms are efficient.

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Differential Equations

License

Copyright (c) 2025 Ali Attia Ali, Amany Saad Mohamed

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How to Cite

Comparative Analysis of the Differential Transform Method and Generalized Fibonacci Collocation Method for Solving Differential Equations. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6734. https://doi.org/10.29020/nybg.ejpam.v18i4.6734