The one-dimensional heat equation subject to a boundary integral specification.

*(English)*Zbl 1139.35352Summary: The problem of solving the one-dimensional parabolic partial differential equation subject to given initial and nonlocal boundary conditions is considered. Several approaches for the numerical solution of this boundary value problem which have been considered in the literature, are reported. New finite difference techniques are proposed for the numerical solution of the one-dimensional heat equation subject to the specification of mass. Numerical examples are given at the end of this paper to compare the efficiency of the new techniques. Some specific applications in various engineering models are introduced.

##### MSC:

35K05 | Heat equation |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

35K20 | Initial-boundary value problems for second-order parabolic equations |

45K05 | Integro-partial differential equations |

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\textit{M. Dehghan}, Chaos Solitons Fractals 32, No. 2, 661--675 (2007; Zbl 1139.35352)

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