Numerical treatment of moving and free boundary value problems with the tau method.

*(English)*Zbl 0999.65110Summary: This paper reports numerical experiments on the implementation of the operational formulation of the tau method for moving and free boundary value problems. We consider problems defined by linear and nonlinear ordinary differential equations and by linear partial differential equations. We compare the accuracy attainable with the technique introduced in this paper with that of standard numerical techniques. We find that the tau method provides accurate results, even using approximations of a low degree.

##### MSC:

65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |

35K15 | Initial value problems for second-order parabolic equations |

35R35 | Free boundary problems for PDEs |

80A22 | Stefan problems, phase changes, etc. |

##### Keywords:

moving boundary problems; free boundary problems; tau method; melting; freezing; numerical experiments
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\textit{M. H. AliAbadi} and \textit{E. L. Ortiz}, Comput. Math. Appl. 35, No. 8, 53--61 (1998; Zbl 0999.65110)

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##### References:

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