Math. Model. Nat. Phenom.
Volume 14, Number 3, 2019
Fractional order mathematical models in physical sciences
|Number of page(s)||12|
|Published online||28 May 2019|
A new approach to capture heterogeneity in groundwater problem: An illustration with an Earth equation
Institute for Groundwater Studies, Faculty of Natural and Agricultural Science, University of Free State,
Bloemfontein, South Africa.
2 Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia.
* Corresponding author: AtanganaA@ufs.ac.za
Accepted: 3 December 2018
One of the major problem faced in modeling groundwater flow problems is perhaps how to capture heterogeneity of the geological formation within which the flow takes place. In this paper, we suggested applied a newly established approach to model real world problems that combines the concept of stochastic modeling in which parameters inputs are converted into distributions and the time differential operator is replaced by non-local differential operators. We illustrated this method with the Earth equation of groundwater recharge. For each case, we provided numerical and exact solution using the newly established numerical scheme and Laplace transform. We presented some numerical simulations. The numerical graphical representations let no doubt to think that this approach is the future way of modeling complex problems.
Mathematics Subject Classification: 34A08 / 26A33 / 34K28
Key words: Stochastic approach / non-local differential operators / Earth equation
© EDP Sciences, 2019
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