Approximation of the modified error function

作者：Ceretani Andrea N; Salva Natalia N^*; Tarzia Domingo A

来源：Applied Mathematics and Computation, 2018, 337: 607-617.

DOI：10.1016/j.amc.2018.05.054

• Modified error function
• Error function
• Phase-change problem
• Temperature-dependent thermal conductivity
• Nonlinear second order ordinary differential equation

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 delta, 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 delta. Accurate approximations are obtained through functions involving error and exponential functions only. For the special case in which delta 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 delta goes to zero.

• 出版日期2018-11-15