THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Nahid Fatima

,

Kamal Shah

,

Thabet Abdeljawad

POROUS MEDIUM EQUATION WITH ELZAKI TRANSFORM HOMOTOPY PERTURBATION

ABSTRACT
We have shown how to solve 1-D fourth order parabolic linear PDE with varable coefficients in this article. We have applied the Elzaki transform homotopy pertur­bation method. It is used in conjunction with the homotopy perturbation approach in this method. To further showcase the Elzaki transform-homotopy perturbation technique's competence and reliability, we have provided solution the parabolic linear PDE. It was found that both HPM and Laplace decomposition method were similar when compared to resulting analytical solutions. Results suggest that the Elzaki transform in conjunction with the homotopy perturbation technique is capa­ble and practicable for use in these cases.
KEYWORDS
homotopy perturbation method, linear PDE, Elzaki transform
PAPER SUBMITTED: 2022-02-01
PAPER REVISED: 2022-03-04
PAPER ACCEPTED: 2022-03-14
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1001F
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [1 - 8]
REFERENCES
  1. Jafari, H., et al., Application of Homotopy Perturbation Method for Solving Gas Dynamics Equation, Appl. Math. Science, 2 (2008), 48, pp. 2393-2396
  2. Elzaki, T. M., Hilal, E. M. A., Homotopy Perturbation and ELzaki Transform for solving Non-Linear Partial Differential Equations, Mathematical Theory and Modelling, 2 (2012), 3, pp. 33-42
  3. Fatima, N., The Study of Heat Conduction Equation by Homotopy Perturbation Method, SN Comput. Sci. 3 (2022), 65
  4. Fatima, N., Solution of Linear Partial Differential Equation with Variable Coefficient by HPM, International Journal of Mechanical Engineering, 7 (2022), 2 pp. 3564-3568
  5. Jafari, H. et al., A New Approach to the Gas Dynamics Equation: An Application of the Variational Iteration Method, Applied Mathematical Sciences, 2 (2008) 48, pp. 2397-2400
  6. Matinfar, M., et al., Variational Iteration Method for Exact Solution of Gas Dynamics Equation Using He's Polynomials, Bulletin of Mathematical Analysis and Applications, 3 (2011), 3, pp. 50-55
  7. Fatima, N., Solution of Gas Dynamic and Wave Equations with VIM, Advances in Fluid Dynamics, Lecture Notes in Mechanical Engineering, Springer, Singapore, Singapore, 2021, pp. 81-91
  8. Evans, D. J., Bulut, H., A New Approach to the Gas Dynamics Equation: An Application of the Decomposition Method, Appl. Comp. Math., 79 (2002), 7, pp. 817- 822
  9. Aminikhah, H., Jamalian, A., Dynamic Equation, International Journal of Partial Differential Equations, 2013 (2013), ID846749
  10. Elzaki T. M., Elzaki, S. M., Applications of New Transform "ELzaki Transform" to Partial Differential Equations, Global Journal of Pure and Applied Mathematics, 7 (2011), 1, pp. 65-70
  11. Elzaki T. M., The New Integra Transform "ELzakiTransform", Global Journal of Pure and Applied Mathematics, 7 (2011), 1, pp. 57-64
  12. Shah, K., et al. Analytical Solutions of Fractional Order Diffusionequations by Natural Transform Method, Iran. J. Sci. Technol, Trans. Sci., 42 (2018), Oct., pp. 1479-1490
PDF VERSION [DOWNLOAD]
Porous medium equation with Elzaki transform homotopy perturbation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence