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Zafar Projected Differential Transform and laplace projected differential transform methods as exact solution methods for Klein- Gordon equations

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General Information
Title
Zafar Projected Differential Transform and laplace projected differential transform methods as exact solution methods for Klein- Gordon equations
Type
Article
Main Author
Gbodogbe, Sunday Oluwafemi
Additional Authors
  • Loyinmi, Adedapo Chris
Subject
QA Mathematics
ISSN
2289-7070 / e-ISSN 2462-2451
Language Code
eng
Bibliographic Details
Place of Production
Tanjong Malim
Publisher
UPSI Press
Year of publication
2026
Notes
EDUCATUM JSMT, 13(1),2026
Degree Type
Others
Corporate Name
Perpustakaan Tuanku Bainun

Abstract

In this study, we propose two innovative numerical methods for solving Klein- Gordon equations: the Zafar Projected Differential Transform Method (ZPDTM) and the Laplace Projected Differential Transform Method (LPDTM). By integrating the Zafar and Laplace transforms respectively with the Projected Differential Transform Method, these approaches offer improved computational efficiency and enhanced solution accuracy. The performance of both methods is demonstrated through their application to linear and nonlinear forms of the Klein-Gordon equation, showing strong agreement with exact solutions and reduced computational overhead. These results highlight the versatility and reliability of ZPDTM and LPDTM in addressing complex differential models encountered in physics and engineering. Keywords Zafar Transform; Laplace Transform; Projected Differential Transform; Klein- Gordon equations; Exact solution

References

Ita, B. I., & Tchoua, P. (2013). The solution of nonlinear Klein-Gordon equation using

Reduced differential transform method. Res. J. Phys. Sci, 1, 21-23.

 

Gbodogbe, S. O. (2025). Harmonizing epidemic dynamics: A fractional calculus approach

to optimal control strategies for cholera transmission. Scientific African, 27, e02545.

 

Giliberti, M., & Lovisetti, L. (2024). The Klein–Gordon Equation. In Old Quantum Theory

and Early Quantum Mechanics: A Historical Perspective Commented for the Inquiring

Reader (pp. 571-609). Cham: Springer Nature Switzerland.

 

Loyinmi, A. C., Lawal, O. W., & Sottin, D. O. (2017). Reduced differential transform

method for solving partial integro-differential equation. J. Niger. Assoc. Math. Phys, 43,

37-42.

 

Kanth, A. R., & Aruna, K. (2009). Differential transform method for solving the linear and

nonlinear Klein–Gordon equation. Computer Physics Communications, 180(5), 708-711.

 

Loyinmi, A. C. (2024). Analysis of two hybrid schemes to solve the Benjamin-Bona-

Mahony (BBM) equation. Kathmandu University Journal of Science, Engineering and

Technology, 18(1), 1-15.

 

Singh, J., Kumar, D., & Rathore, S. (2012). Application of homotopy perturbation

transform method for solving linear and nonlinear Klein-Gordon equations. Journal of

Information and Computing Science, 7(2), 131-139.

 

Keskin, Y., Servi, S., & Oturanç, G. (2011, July). Reduced differential transform method

for solving Klein Gordon equations. In Proceedings of the World Congress on engineering

(Vol. 1, p. 2011).

 

Schiff, J. L. (1999). The Laplace transform: theory and applications. Springer Science &

Business Media.

 

Loyinmi, A. C., & Lawal, O. W. (2011). The asymptotic solution for the steady variableviscosity

free convection flow on a porous plate. Journal of the Nigerian Association of

Mathematical Physics, 19.

 

Akinfe, T. K., & Loyinmi, A. C. (2022). An improved differential transform scheme

implementation on the generalized Allen–Cahn equation governing oil pollution dynamics

in oceanography. Partial Differential Equations in Applied Mathematics, 6, 100416.

 

Loyinmi, A. C., Erinle-Ibrahim, L. M., & Adeyemi, A. E. (2017). The new iterative method

(NIM) for solving telegraphic equation. J. Niger. Assoc. Math. Phys, 43, 31-36.

 

Idowu, K. O., & Loyinmi, A. C. (2023). THE ANALYTIC SOLUTION OF NON-LINEAR

BURGERS–HUXLEY EQUATIONS USING THE TANH METHOD. Al-Bahir journal for

Engineering and Pure Sciences, 3(1), 8.

 

Lawal, O. W., Loyinmi, A. C., & Sowumi, S. O. (2017). Homotopy perturbation algorithm

using Laplace transform for linear and nonlinear ordinary delayed differential equation. J.

Niger. Assoc. Math. Phys, 41, 27-34.

 

Idowu, K. O., Akinwande, T. G., Fayemi, I., Adam, U. M., & Loyinmi, A. C. (2023).

Laplace Homotopy Perturbation Method (LHPM) for solving systems of N-dimensional

non-linear partial differential equation. Al-Bahir Journal for Engineering and Pure

Sciences, 3(1), 11-27.

 

Loyinmi, A. C., Sanyaolu, M. D., & Gbodogbe, S. (2025). Exploring the Efficacy of the

Weighted Average Method for Solving Nonlinear Partial Differential Equations: A Study

on the Burger-Fisher Equation. EDUCATUM Journal of Science, Mathematics and

Technology, 12(1), 60-79.

 

Yaseen, M., & Samraiz, M. (2012). The modified new iterative method for solving linear

and nonlinear Klein-Gordon equations. Applied Mathematical Sciences, 6(60), 2979-2987.

 

Idowu, K. O., & Loyinmi, A. C. (2023). THE ANALYTIC SOLUTION OF NON-LINEAR

BURGERS–HUXLEY EQUATIONS USING THE TANH METHOD. Al-Bahir journal for

Engineering and Pure Sciences, 3(1), 8.

 

Loyinmi, A. C., & Idowu, K. O. (2023). Semi-analytic approach to solving rosenau-hyman

and korteweg-de vries equations using integral transform. Tanzania Journal of Science,

49(1), 26-40.

 

Loyinmi, A. C., Oredein, A. I., & Prince, S. U. (2018). Homotopy adomian decomposition

method for solving linear and nonlinear partial differential equations. Tasued J. Pure Appl.

Sci, 1, 254-260.

 

Loyinmi, A. C., & Lawal, O. W. (2011). The asymptotic solution for the steady variableviscosity

free convection flow on a porous plate. Journal of the Nigerian Association of

Mathematical Physics, 19.

 

Lawal, O. W., & Loyinmi, A. C. (2012). Magnetic and porosity effect on MHD flow of a

dusty visco-elastic fluid through horizontal plates with heat transfer. J. Niger. Assoc. Math.

Phys, 21, 95-104.

 

Khan, M., Hussain, M., Jafari, H., & Khan, Y. (2010). Application of Laplace

decomposition method to solve nonlinear coupled partial differential equations. World

Applied Sciences Journal, 9(1), 13-19.

 

Loyinmi, A. C. (2024). An advanced Taylor’s Series Method to Obtain New Exact

Travelling Waves Solutions of the Real-Valued Stochastic Ginzburg-Landau Equation.

Journal of Science and Information Technology, 18(1), 137-156.


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