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Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Solving porous medium equation using SEE transform homotopy perturbation method

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pp. 1001–1007Vol. 29Issue 4April 2026DOI: 10.47974/JIM-2471XML
Received:
01 Sep 2025
Published Online:
21 Mar 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2471
Pages:
1001–1007

Abstract

This work innovatively solves the porous medium equation for the first time by using what is now called the “SEE transform.” This newly devised integral transform is employed in tandem with the homotopy perturbation method. The nonlinear part of the porous medium equations is skillfully treated by the homotopy perturbation approach, and solution to these equations are constructed with several examples to demonstrate the efficiency and dependability of combining the homotopy perturbation method with the SEE transform. Further outcome underscores the efficiency and practical appropriateness of combining the SEE transform with the homotopy perturbation technique in addressing these challenges.

Keywords

Subject Classifications

44A1035A2235Q79

References

[1] A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations. Boca Raton, FL, USA: Chapman & Hall/CRC Press (2004).
[2] J. L. Vázquez, The Porous Medium Equation: Mathematical Theory. Oxford, U.K.: Clarendon Press, Oxford Science Publications, pp. 1–28 (2007).
[3] V. G. Gupta and S. Gupta, “Homotopy perturbation transform method for solving heat-like and wave-like equation with variable coefficient,” International Journal of Mathematical Archive, vol. 2, no. 9, pp. 1582–1590 (2011).
[4] A. Ghorbani, “Beyond Adomian polynomials: He polynomials,” Chaos, Solitons & Fractals, vol. 39, no. 3, pp. 1486–1492 (2009).
[5] I. Hashim, M. S. M. Noorani, R. Ahmad, S. A. Bakar, E. S. Ismail, and A. M. Zakaria, “Accuracy of the Adomian decomposition method applied to the Lorenz system,” Chaos, Solitons & Fractals, vol. 28, no. 5, pp. 1149–1158 (2006).
[6] N. H. Sweilam and M. M. Khader, “Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method,” Computers & Mathematics with Applications, vol. 58, nos. 11–12, pp. 2134–2141 (2009).
[7] P. R. Sharma and G. Methi, “Application of homotopy perturbation method to partial differential equations,” Asian Journal of Mathematics and Statistics, vol. 4, no. 3, pp. 140–150 (2011).
[8] E. Kuffi, E. Mansour, and A. J. Issa, “SEE transform technique in control theory,” Journal of Kufa for Mathematics and Computer, vol. 11, no. 2, pp. 147–149 (2024).
[9] D. Mishra, V. H. Pradhan, and M. N. Mehta, “Solution of porous medium equation by homotopy perturbation transform method,” International Journal of Engineering Research and Applications, vol. 2, no. 3, pp. 2041–2046 (2012).
[10] K. S. Aboodh, “Solving porous medium equation using Aboodh transform homotopy perturbation method,” American Journal of Applied Mathematics, vol. 4, no. 6, pp. 271–276 (2016).
[11] Y. Mahajan and H. Nagar, “Composition formulas for Saigo K-fractional operator associated with generalized K-Bessel Maitland function,” Journal of Interdisciplinary Mathematics, vol. 27, no. 8, pp. 1861–1867 (2024).
[12] P. Gautam, H. Nagar, and S. Sharma, “The Marichev-Saigo-Maeda fractional calculus operator pertaining to the generalized multivariate Mittag-Leffler function,” Journal of Interdisciplinary Mathematics, vol. 27, no. 8, pp. 1853–1860 (2024).

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