Difference schemes for time-dependent heat conduction models with delay

Castro, María Ángeles; Rodríguez, Francisco; Cabrera, Juan Luis; Martín, J.A.

doi:10.1080/00207160.2013.779371

Cited by 9 publications

(3 citation statements)

References 30 publications

(42 reference statements)

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“…Fourth, we study the initial boundary value problem (26) for multidimensional semilinear delay hyperbolic equations. The discretization of problem (23) is provided in two steps.…”

Section: Theorem 12 For the Solutions Of The Elliptic Difference Promentioning

confidence: 99%

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Bounded Solutions of Semilinear Time Delay Hyperbolic Differential and Difference Equations

Ashyralyev

Agirseven

2019

Mathematics

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In this paper, we study the initial value problem for a semilinear delay hyperbolic equation in Hilbert spaces with a self-adjoint positive definite operator. The mean theorem on the existence and uniqueness of a bounded solution of this differential problem for a semilinear hyperbolic equation with unbounded time delay term is established. In applications, the existence and uniqueness of bounded solutions of four problems for semilinear hyperbolic equations with time delay in unbounded term are obtained. For the approximate solution of this abstract differential problem, the two-step difference scheme of a first order of accuracy is presented. The mean theorem on the existence and uniqueness of a uniformly bounded solution of this difference scheme with respect to time stepsize is established. In applications, the existence and uniqueness of a uniformly bounded solutions with respect to time and space stepsizes of difference schemes for four semilinear partial differential equations with time delay in unbounded term are obtained. In general, it is not possible to get the exact solution of semilinear hyperbolic equations with unbounded time delay term. Therefore, numerical results for the solution of difference schemes for one and two dimensional semilinear hyperbolic equation with time delay are presented. Finally, some numerical examples are given to confirm the theoretical analysis.

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“…Fourth, we study the initial boundary value problem (26) for multidimensional semilinear delay hyperbolic equations. The discretization of problem (23) is provided in two steps.…”

Section: Theorem 12 For the Solutions Of The Elliptic Difference Promentioning

confidence: 99%

“…Castro, Rodriguez, Cabrera, and Martin [26] developed an explicit finite difference scheme for a model with coefficients variable in time and studied their properties of convergence and stability.…”

Section: Introductionmentioning

confidence: 99%

Bounded Solutions of Semilinear Time Delay Hyperbolic Differential and Difference Equations

Ashyralyev

Agirseven

2019

Mathematics

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“…It should be noted that Fourier transforms can also be used in time-dependent problems (e.g., [29,30]), and the approach of this work could also be useful for timedependent DPL models, which have already been proposed [31].…”

Section: Introductionmentioning

confidence: 99%

Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium

Castro¹,

Rodríguez²,

Escolano³

et al. 2013

Abstract and Applied Analysis

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Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.

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The Method of Fractional Steps for the Numerical Solution of a Multidimensional Heat Conduction Equation with Delay for the Case of Variable Coefficient of Heat Conductivity

Lekomtsev

2020

Springer Proceedings in Mathematics &Amp; Statistics

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Difference schemes for time-dependent heat conduction models with delay

Cited by 9 publications

References 30 publications

Bounded Solutions of Semilinear Time Delay Hyperbolic Differential and Difference Equations

Bounded Solutions of Semilinear Time Delay Hyperbolic Differential and Difference Equations

Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium

The Method of Fractional Steps for the Numerical Solution of a Multidimensional Heat Conduction Equation with Delay for the Case of Variable Coefficient of Heat Conductivity

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