Numerical solution of the heat equation with nonlocal boundary conditions
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In this article, the unconditional stability of the θ-method for the heat equation with nonlocal boundary conditions is proved for θ⩾ 1 2, subject to a condition that is much weaker than the one assumed in a paper by Ekolin.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1999-10-15 and is currently open access. It has received 82 citations till now. The article focuses on the topics: Mixed boundary condition & Boundary value problem.read more
Citations
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On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation
TL;DR: In this article, a non-classical hyperbolic boundary value problem with non-local boundary conditions is studied. But, most of the articles were directed to the second-order parabolic equation, particularly to heat conduction equation.
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The one-dimensional heat equation subject to a boundary integral specification
TL;DR: In this article, the problem of solving the one-dimensional parabolic partial differential equation subject to given initial and non-local boundary conditions is considered, and several approaches for the numerical solution of this boundary value problem which have been considered in the literature, are reported.
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A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications
TL;DR: In this article, the numerical solution of the one-dimensional parabolic equation subject to the specification of mass, which have been considered in the literature, is reported. And the performance of the proposed algorithm, considering a test problem, is investigated.
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Efficient techniques for the second-order parabolic equation subject to nonlocal specifications
TL;DR: In this article, various approaches for the numerical solution of the one-dimensional heat equation subject to the specification of mass which have been considered in the literature, are reported, and some specific applications in engineering models are introduced.
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On the solution of the non-local parabolic partial differential equations via radial basis functions
Mehdi Tatari,Mehdi Dehghan +1 more
TL;DR: In this article, an efficient collocation method is proposed for solving non-local parabolic partial differential equations using radial basis functions, and the results are compared with some existing methods.
References
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Updating the inverse of a matrix
TL;DR: The history of these fomulas is presented and various applications to statistics, networks, structural analysis, asymptotic analysis, optimization, and partial differential equations are discussed.
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The One-Dimensional Heat Equation
TL;DR: In this paper, Browder et al. considered the initial-boundary value problem for the semi-infinite strip with temperature and flux-flux-boundaries specification.
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TL;DR: In this paper, it was shown that modified forms of (P) remain true within both the quasi-static and the dynamic theories of coupled linear thermoelasticity, and also within certain theories which replace the parabolic heat equation by a linear hyperbolic equation and thereby ensure that temperature disturbances propagate at finite speed.
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A decreasing property of solutions of parabolic equations with applications to thermoelasticity
TL;DR: In this paper, the authors considered the case where the faces of the slab were maintained at the reference temperature and clamped, that is to say the slab was not clamped.