Comparative Study of the Differential Transform Method and the α-Parametrized Differential Transform Method for Boundary Value Problems

Authors

  • Siti Ainor Mohd Yatim School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia
  • Junaid Ali Department of Mathematics and statistics, University of Agriculture Faisalabad, Pakistan
  • Muhammad Zeeshan Department of Mathematics and statistics, University of Agriculture Faisalabad, Pakistan
  • Shah Zeb School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia
  • Muhammad Bilal Department of Mathematics, University of Layyah, 31200, Pakistan
  • Ubaid Ur Rehman Department of Mathematics, Riphah International University Faisalabad Campus 38000, Pakistan
  • Maytham Nazzal Barbar Al-Abedi School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia

Keywords:

Boundary value problems, differential transform method, α-parametrized differential transform method

Abstract

In this paper, the differential transform method (DTM) and the -parametrized differential transform method (–PDTM) are studied and linked by applying them to boundary value problems. Numerical solution obtained from the examples were compared with that of exact solution. The absolute error obtained from this evaluation showed that DTM has lower error margin and rapid convergence when likened to –PDTM. Tables for discrete and exact solutions were presented to show the efficiency of the two methods. Numerical computations were added and solution obtained showed that DTM is very precise and proficient method in distinction to –PDTM.

Author Biographies

Siti Ainor Mohd Yatim, School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia

ainor@usm.my

Junaid Ali, Department of Mathematics and statistics, University of Agriculture Faisalabad, Pakistan

ustaadjunaid88@gmail.com

Muhammad Zeeshan, Department of Mathematics and statistics, University of Agriculture Faisalabad, Pakistan

zs8036125@gmail.com

Shah Zeb, School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia

shahzeb@student.usm.my

Muhammad Bilal, Department of Mathematics, University of Layyah, 31200, Pakistan

m.bilal6979@gmail.com

Ubaid Ur Rehman, Department of Mathematics, Riphah International University Faisalabad Campus 38000, Pakistan

ubaid.rehman367@gmail.com

Maytham Nazzal Barbar Al-Abedi, School of Distance Education, Universiti Sains Malaysia, 11800 Penang, Malaysia

alabedi@student.usm.my

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Published

2025-09-13

How to Cite

Mohd Yatim, S. A., Ali, J., Zeeshan, M., Zeb, S., Bilal, M., Rehman, U. U., & Al-Abedi, M. N. B. (2025). Comparative Study of the Differential Transform Method and the α-Parametrized Differential Transform Method for Boundary Value Problems. Warisan Journal of Mathematical Sciences and Engineering , 2(1), 1–10. Retrieved from https://warisanunggul.my/index.php/wjmse/article/view/10

Issue

Vol. 2 No. 1: September (2025)

Section

Articles