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Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions

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  • Carr, Elliot J.
  • March, Nathan G.

Abstract

We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the semi-analytical method, relative to the number of eigenvalues, is investigated and the effect of varying the interface conditions on the solution behaviour is explored. Numerical experiments demonstrate that solutions can be computed using the new semi-analytical method that are more accurate and more efficient than the unified transform method of Sheils [Appl. Math. Model., 46:450–464, 2017]. Furthermore, unlike classical analytical solutions and the unified transform method, only the new semi-analytical method is able to correctly treat problems with both time-varying external boundary conditions and a large number of layers. The paper is concluded by replicating solutions to several important industrial, environmental and biological applications previously reported in the literature, demonstrating the wide applicability of the work.

Suggested Citation

  • Carr, Elliot J. & March, Nathan G., 2018. "Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 286-303.
    • Handle: RePEc:eee:apmaco:v:333:y:2018:i:c:p:286-303
    DOI: 10.1016/j.amc.2018.03.095
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    Cited by:

    1. A. Itkin & A. Lipton & D. Muravey, 2021. "Multilayer heat equations: application to finance," Papers 2102.08338, arXiv.org.
    2. Taneco-Hernández, M.A. & Morales-Delgado, V.F. & Gómez-Aguilar, J.F., 2019. "Fundamental solutions of the fractional Fresnel equation in the real half-line," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 807-827.
    3. Moisés A. C. Lemos & Camilla T. Baran & André L. B. Cavalcante & Ennio M. Palmeira, 2023. "A Semi-Analytical Model of Contaminant Transport in Barrier Systems with Arbitrary Numbers of Layers," Sustainability, MDPI, vol. 15(23), pages 1-18, November.
    4. Andrey Itkin & Alexander Lipton & Dmitry Muravey, 2021. "Multilayer heat equations and their solutions via oscillating integral transforms," Papers 2112.00949, arXiv.org, revised Dec 2021.
    5. Itkin, Andrey & Lipton, Alexander & Muravey, Dmitry, 2022. "Multilayer heat equations and their solutions via oscillating integral transforms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).

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