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On boundary immobilization for one-dimensional Stefan-type problems with a moving boundary having initially parabolic-logarithmic behaviour

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  • Vynnycky, M.

Abstract

In this paper, a recent one-dimensional Stefan-type model for the sorption of a finite amount of swelling solvent in a glassy polymer is revisited, with a view to formalizing the application of the boundary immobilization method to this problem. The key difficulty is that the initial behaviour of the moving boundary is parabolic-logarithmic, rather than algebraic, which has more often than not been the case in similar problems. A small-time analysis of the problem hints at how the usual boundary immobilization formalism can be recovered, and this is subsequently verified through numerical experiments. The relevance of these results to other moving boundary problems from the literature is also discussed.

Suggested Citation

  • Vynnycky, M., 2023. "On boundary immobilization for one-dimensional Stefan-type problems with a moving boundary having initially parabolic-logarithmic behaviour," Applied Mathematics and Computation, Elsevier, vol. 444(C).
    • Handle: RePEc:eee:apmaco:v:444:y:2023:i:c:s0096300322008712
    DOI: 10.1016/j.amc.2022.127803
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    1. J. D. Evans & R. Kuske & Joseph B. Keller, 2002. "American options on assets with dividends near expiry," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 219-237, July.
    2. Mitchell, S.L. & Vynnycky, M., 2021. "An accuracy-preserving numerical scheme for parabolic partial differential equations subject to discontinuities in boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    3. R. Company & V. N. Egorova & L. Jódar, 2014. "Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, April.
    4. Florio, B.J. & Vynnycky, M. & Mitchell, S.L. & O’Brien, S.B.G., 2015. "Mould-taper asymptotics and air gap formation in continuous casting," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1122-1139.
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