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Study and analysis of nonlinear (2+1)-dimensional solute transport equation in porous media

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  • Singh, Anup
  • Das, Subir
  • Ong, S.H.

Abstract

In the present endeavour, the shifted Legendre collocation method is extended to obtain the solution of nonlinear fractional order (2+1)-dimensional advection–reaction–diffusion solute transport equation. The variations of solute concentration of the model for different fractional order space and time derivatives are presented graphically for various particular cases. The main feature of the present contribution is the graphical exhibitions of the effects of advection term, reaction term and fractional-order parameters on the solution profile. To authenticate the effectiveness of the method, a drive has been taken to compare the obtained results with the existing analytical results of the integer-order form of the considered model through error analysis which are displayed in tabular and pictorial forms.

Suggested Citation

  • Singh, Anup & Das, Subir & Ong, S.H., 2022. "Study and analysis of nonlinear (2+1)-dimensional solute transport equation in porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 491-500.
    • Handle: RePEc:eee:matcom:v:192:y:2022:i:c:p:491-500
    DOI: 10.1016/j.matcom.2021.08.022
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    References listed on IDEAS

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    1. Huamin Zhang & Feng Ding, 2013. "On the Kronecker Products and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, June.
    2. Zhang, Juan & Zhang, Xindong & Yang, Bohui, 2018. "An approximation scheme for the time fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 305-312.
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    Cited by:

    1. Biswas, Chetna & Singh, Anup & Chopra, Manish & Das, Subir, 2023. "Study of fractional-order reaction-advection-diffusion equation using neural network method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 15-27.
    2. Vsevolod Bohaienko & Fasma Diele & Carmela Marangi & Cristiano Tamborrino & Sebastian Aleksandrowicz & Edyta Woźniak, 2023. "A Novel Fractional-Order RothC Model," Mathematics, MDPI, vol. 11(7), pages 1-16, March.

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