Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutions

B. Tomas Johansson, Daniel Lesnic, Thomas Reeve, Thomas Reeve

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional parabolic inverse Cauchy–Stefan problem, where boundary data and the initial condition are to be determined from the Cauchy data prescribed on a given moving interface. In [B.T. Johansson, D. Lesnic, and T. Reeve, A method of fundamental solutions for the one-dimensional inverse Stefan Problem, Appl. Math Model. 35 (2011), pp. 4367–4378], the inverse Stefan problem was considered, where only the boundary data is to be reconstructed on the fixed boundary. We extend the MFS proposed in Johansson et al. (2011) and show that the initial condition can also be simultaneously recovered, i.e. the MFS is appropriate for the inverse Cauchy-Stefan problem. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be efficiently obtained with small computational cost.
Original languageEnglish
Pages (from-to)659-677
Number of pages19
JournalInverse Problems in Science and Engineering
Volume19
Issue number5
DOIs
Publication statusPublished - 2011
Event5th International Conference on Inverse Problems: Modeling and Simulation - Antalya, Turkey
Duration: 24 May 201029 May 2010

Keywords

  • heat conduction
  • method of fundamental solutions
  • inverse Cauchy–Stefan problem

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