### Abstract

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Original language | English |
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Number of pages | 15 |

Journal | Journal of Engineering Mathematics |

Volume | Early online |

Early online date | 4 Apr 2016 |

DOIs | |

Publication status | E-pub ahead of print - 4 Apr 2016 |

### Bibliographical note

-### Keywords

- boundary integral equations of the first kind
- discrete projection method
- exterior 3-dimensional domain
- heat equation
- Laguerre transformation

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## Cite this

*Journal of Engineering Mathematics*,

*Early online*. https://doi.org/10.1007/s10665-016-9858-6