An Innovative Analytical Result of Two-Dimensional Heat Equation Using Joint Mechanism of Natural Transform and Adomian Decomposition Method

Authors

  • Muhammad Usman Department of Mathematics, University of Malakand at Chakdara, Dir (Lower), KP, Pakistan)
  • Hidayat Ullah Khan Department of Mathematics, University of Malakand, Dir (Lower), KP
  • Muhammad Sarwar Department of Mathematics, University of Malakand, Dir (Lower), KP
  • Nahid Fatima Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia
  • Kamaleldin Abodayeh Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6051

Keywords:

2D Heat Equation, Adomian Decomposition Method, Natural transform

Abstract

This research article has put forward an innovative analytical result of the 2D heat equation having a source term. The aforesaid non-homogenous PDE is solved through a new hybrid mechanism. whereas the technique supports the solution process, commencing with the parametric form of the 2D heat equation. Furthermore, this hybrid mechanism which consists of Natural transform (NT) and a series solution method of Adomian decomposition method (ADM) is applied properly. Next, the solution that is obtained for the unknown function is presented in series form. During the computational process, it was observed that the proposed mechanism is less time-consuming and efficient with accurate results. Which shows that the mechanism (proposed mechanism) makes a very useful contribution to the analytical solution of the 2D heat equation. The paper is properly supported with appropriate examples to verify the claim.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Differential Equations

License

Copyright (c) 2025 Muhammad Usman, Hidayat Ullah Khan, Muhammad Sarwar, Nahid Fatima , Kamaleldin Abodayeh

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How to Cite

An Innovative Analytical Result of Two-Dimensional Heat Equation Using Joint Mechanism of Natural Transform and Adomian Decomposition Method. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6051. https://doi.org/10.29020/nybg.ejpam.v18i2.6051