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International Conference on Applied and Computational Mathematics

ICACM 2018: Mathematical Modeling and Computational Tools pp 239–248Cite as

Numerical Solution of Space and Time Fractional Advection–Diffusion Equation by Meshless Approach

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 320))

Abstract

In this paper, fractional version of advection–diffusion equation (FADE) has been considered for the numerical solution. It is acquired from the classical advection–diffusion equation (ADE) by substituting the space and time derivatives with a generalized Caputo fractional derivative. Moreover, we have proposed novel discretization for space and time using radial basis functions and Chebyshev polynomials, respectively. The proposed scheme is truly meshless thereby able to manage both space and time fractional derivatives simultaneously with appropriate boundary conditions. Lastly, we have discussed numerical example to affirm this proposed scheme whilst revealing the accuracy and performance of the same.

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Authors and Affiliations

  1. S. V. National Institute of Technology, Surat, India

    Hitesh Bansu & Sushil Kumar

Authors
  1. Hitesh Bansu
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  2. Sushil Kumar
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Correspondence to Hitesh Bansu .

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Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India

    Somnath Bhattacharyya

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India

    Jitendra Kumar

  3. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, India

    Koeli Ghoshal

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Bansu, H., Kumar, S. (2020). Numerical Solution of Space and Time Fractional Advection–Diffusion Equation by Meshless Approach. In: Bhattacharyya, S., Kumar, J., Ghoshal, K. (eds) Mathematical Modeling and Computational Tools. ICACM 2018. Springer Proceedings in Mathematics & Statistics, vol 320. Springer, Singapore. https://doi.org/10.1007/978-981-15-3615-1_16

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