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**Constrained integral method for solving moving boundary problems.**
*(English)*
Zbl 0619.65125

In solving a moving boundary problem by the conventional integral method, the various parameters in the choice of a temperature/concentration profile are expressed in terms of the position of the moving boundary only, while in the present method they are expressed as functions of the position of the moving boundary plus an additional parameter at the fixed surface. This new parameter is taken to be the space derivative, when a Dirichlet condition is prescribed at the fixed end, or to be the function value when a Neumann-type condition is prescribed there. By doing so a control is provided at both ends, i.e. the moving boundary as well as the fixed end. Finally two simultaneous first-order differential equations are obtained which give the position of the moving boundary and the value of the unknown additional parameter in an implicit manner. Two sample problems with different types of boundary conditions at the fixed end are considered for testing the suggested method. The results seem to be in very good agreement with those due to earlier authors who have solved the problem using other techniques.

### MSC:

65Z05 | Applications to the sciences |

65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |

35K05 | Heat equation |

80A17 | Thermodynamics of continua |

35R35 | Free boundary problems for PDEs |

### Keywords:

Stefan problem; moving boundary problem; integral method; temperature/concentration profile; parameter; Dirichlet condition; Neumann-type condition; control
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\textit{R. S. Gupta} and \textit{N. C. Banik}, Comput. Methods Appl. Mech. Eng. 67, No. 2, 211--221 (1988; Zbl 0619.65125)

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### References:

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