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Approximation of the modified error function

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  • Ceretani, Andrea N.
  • Salva, Natalia N.
  • Tarzia, Domingo A.

Abstract

In this article, we obtain explicit approximations of the modified error function introduced in Cho and Sunderland (1974), as part of a Stefan problem with a temperature-dependent thermal conductivity. This function depends on a parameter δ, which is related to the thermal conductivity in the original phase-change process. We propose a method to obtain approximations, which is based on the assumption that the modified error function admits a power series representation in δ. Accurate approximations are obtained through functions involving error and exponential functions only. For the special case in which δ assumes small positive values, we show that the modified error function presents some characteristic features of the classical error function, such as monotony, concavity, and boundedness. Moreover, we prove that the modified error function converges to the classical one when δ goes to zero.

Suggested Citation

  • Ceretani, Andrea N. & Salva, Natalia N. & Tarzia, Domingo A., 2018. "Approximation of the modified error function," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 607-617.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:607-617
    DOI: 10.1016/j.amc.2018.05.054
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    References listed on IDEAS

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    1. Barret L. Kurylyk & Masaki Hayashi, 2016. "Improved Stefan Equation Correction Factors to Accommodate Sensible Heat Storage during Soil Freezing or Thawing," Permafrost and Periglacial Processes, John Wiley & Sons, vol. 27(2), pages 189-203, April.
    2. Gaudiano, Marcos & Torres, Germán Ariel & Turner, Cristina, 2009. "On a convective condition in the diffusion of a solvent into a polymer with non-constant conductivity coefficient," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(3), pages 479-489.
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    Cited by:

    1. Xu, Minghan & Akhtar, Saad & Zueter, Ahmad F. & Alzoubi, Mahmoud A. & Sushama, Laxmi & Sasmito, Agus P., 2021. "Asymptotic analysis of a two-phase Stefan problem in annulus: Application to outward solidification in phase change materials," Applied Mathematics and Computation, Elsevier, vol. 408(C).

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