A method of fundamental solutions for the one-dimensional inverse Stefan problem

B.T. Johansson; D. Lesnic; T. Reeve

doi:10.1016/j.apm.2011.03.005

A method of fundamental solutions for the one-dimensional inverse Stefan problem

B.T. Johansson, D. Lesnic, T. Reeve

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77 Citations (Scopus)

Abstract

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

Original language	English
Pages (from-to)	4367–4378
Number of pages	11
Journal	Applied Mathematical Modelling
Volume	35
Issue number	9
Early online date	21 Mar 2011
DOIs	https://doi.org/10.1016/j.apm.2011.03.005
Publication status	Published - Sept 2011

Keywords

heat conduction
method of fundamental solutions (MFS)
inverse Stefan problem

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10.1016/j.apm.2011.03.005

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abstract = "We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.",

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AU - Lesnic, D.

AU - Reeve, T.

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N2 - We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

AB - We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

KW - heat conduction

KW - method of fundamental solutions (MFS)

KW - inverse Stefan problem

U2 - 10.1016/j.apm.2011.03.005

DO - 10.1016/j.apm.2011.03.005

M3 - Article

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VL - 35

SP - 4367

EP - 4378

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

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ER -

A method of fundamental solutions for the one-dimensional inverse Stefan problem

Abstract

Keywords

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