Numerical solutions of diffusion mathematical models with delay

García, Piqueras; Castro, María Ángeles; Martín, J.A.; Sirvent, Antonio

doi:10.1016/j.mcm.2009.05.015

Cited by 16 publications

(7 citation statements)

References 5 publications

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“…It is not difficult to prove, as was done in [8,Theorem 5] for the constant coefficients case, that under these conditions the scheme defined in Equation (8) is asymptotically stable.…”

Section: A] and The Block Matrixmentioning

confidence: 95%

“…Using finite difference approximations to partial derivatives in Equation (2), as in the classical explicit scheme for the diffusion equation [18, pp. 6-8] or in the explicit scheme for the constant coefficients case [8],…”

Section: Construction Of the Difference Schemementioning

confidence: 99%

“…Difference schemes for parabolic problems with delay have also been proposed (see, e.g. [1,2,19,31]), including problem (2) in the constant coefficients case [8,9]. The aim of this work is the construction of an explicit difference scheme for the time-dependent problem (2)-(4), characterizing its convergence properties.…”

Section: Introductionmentioning

confidence: 99%

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Difference schemes for time-dependent heat conduction models with delay

Castro¹,

Rodríguez²,

Cabrera³

et al. 2013

International Journal of Computer Mathematics

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Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

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“…It is not difficult to prove, as was done in [8,Theorem 5] for the constant coefficients case, that under these conditions the scheme defined in Equation (8) is asymptotically stable.…”

Section: A] and The Block Matrixmentioning

confidence: 95%

Section: Construction Of the Difference Schemementioning

confidence: 99%

See 1 more Smart Citation

Difference schemes for time-dependent heat conduction models with delay

Castro¹,

Rodríguez²,

Cabrera³

et al. 2013

International Journal of Computer Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Later on, several researchers have discussed the stability and a priori error analysis of numerical methods for (1.1)-(1.3) with a constant delay, i.e., τ (t) = t − η(t) = τ with τ > 0 being a real constant. The authors of [13,14] considered the consistence, stability and convergence of an explicit difference scheme and two implicit difference schemes for the Eqs. (1.1)-(1.3) with a constant delay, respectively.…”

Section: Introductionmentioning

confidence: 99%

A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay

Wang

Xiao

2020

J Sci Comput

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In this paper, we derive several a posteriori error estimators for generalized diffusion equation with delay in a convex polygonal domain. The Crank-Nicolson method for time discretization is used and a continuous, piecewise linear finite element space is employed for the space discretization. The a posteriori error estimators corresponding to space discretization are derived by using the interpolation estimates. Two different continuous, piecewise quadratic reconstructions are used to obtain the error due to the time discretization. To estimate the error in the approximation of the delay term, linear approximations of the delay term are used in a crucial way. As a consequence, a posteriori upper and lower error bounds for fully discrete approximation are derived for the first time. In particular, long-time a posteriori error estimates are obtained for stable systems. Numerical experiments are presented which confirm our theoretical results.

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“…The mathematical models appearing in applied sciences such as mathematical biology, chemical diffusions, and fluid mechanics generally consist of partial differential equations. In the literature, many interesting studies in these fields can be found (for instance, see [1][2][3][4][5][6]). Over the last two decades, there has been a growing tendency to model some phenomena as inverse problems.…”

Section: Introductionmentioning

confidence: 99%

A note on the numerical solution of an identification problem for observing two‐phase flow in capillaries

Erdogan

Sazaklioglu

2013

Math Methods in App Sciences

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In this paper, a right‐hand side identification problem for a parabolic equation with an overdetermined condition on an observation point is considered. A first and second order of accuracy difference schemes are constructed for obtaining approximate solutions of the problem that arises in two‐phase flow in capillaries. Stability estimates and numerical results are also established. Copyright © 2013 John Wiley & Sons, Ltd.

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Numerical solutions of diffusion mathematical models with delay

Cited by 16 publications

References 5 publications

Difference schemes for time-dependent heat conduction models with delay

Difference schemes for time-dependent heat conduction models with delay

A Posteriori Error Estimates for Fully Discrete Finite Element Method for Generalized Diffusion Equation with Delay

A note on the numerical solution of an identification problem for observing two‐phase flow in capillaries

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