Solving Time-fractional Order Radon Diffusion Equation in Water by Finite Difference Method

Vijaymala Ghuge; T L Holambe; Bhausaheb Sontakke; Gajanan Shrimangale

doi:10.17485/IJST/v17i19.868

Article

$Solving Time-fractional Order Radon Diffusion Equation in Water by Finite Difference Method$

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i19.868

Year: 2024, Volume: 17, Issue: 19, Pages: 1994-2001

Original Article

Solving Time-fractional Order Radon Diffusion Equation in Water by Finite Difference Method

Vijaymala Ghuge^1*, T L Holambe², Bhausaheb Sontakke³, Gajanan Shrimangale⁴

¹Department of Mathematics, Rashtramata Indira Gandhi College, Jalna, Maharashtra, India
²Department of Mathematics, Late Shankarrao Gutte Gramin Arts, Science and Commerce, Dharmapuri, Beed, Maharashtra, India
³Department of Mathematics, Prathishthan Mahavidyalaya, Paithan, Aurangabad, Maharashtra, India
⁴Department of Mathematics, Mrs. Kesharbai Sonajirao Kshirsagar Alias kaku Arts, Science and Commerce College, Beed, Maharashtra, India

*Corresponding Author
Email: [email protected]

Received Date:21 March 2024, Accepted Date:21 April 2024, Published Date:09 May 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: The aim of this research is to gain a comprehensive understanding of radon diffusion equation in water. Methods: A time fractional radon diffusion equation with Caputo sense is employed to find diffusion dynamics of radon in water medium. The fractional order explicit finite difference technique is used to find its numerical solution. A Python software is used to find numerical solution. Findings: The effect of fractional-order parameters on the distribution and concentration profiles of radon in water has been investigated. Furthermore, we study stability and convergence of the explicit finite difference method. Novelty: The fractional order explicit finite difference method can be used to estimate approximate solution of such fractional order differential equations.

Keywords: Radon Diffusion Equation, Finite Difference Method, Caputo, Fractional Derivative, Python

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Copyright

© 2024 Ghuge et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)