Numerical Method for Solving the Time-Fractional Dual-Phase-Lagging Heat Conduction Equation with the Temperature-Jump Boundary Condition

Ji, Cui-cui; Dai, Weizhong; Sun, Zhi‐zhong

doi:10.1007/s10915-017-0588-3

Cited by 24 publications

(27 citation statements)

References 58 publications

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“…Particularly, in the numerical simulation of direct problem, we make a comparison between our approach and another method. 22 The numerical results shows that our approach can achieve higher convergence order with less grid points and shorter CPU time. In future research, we will consider some other higher order schemes to solve our model, such as the fourth order or sixth order finite difference scheme in temporal direction.…”

Section: Discussionmentioning

confidence: 85%

“…From these tables, it can be found that our approach can achieve higher convergence order with less grid points and shorter CPU time, relative to the method in Ji et al. 22 This advantage is more obvious when dealing with high-dimensional problems.…”

Section: Numerical Examplesmentioning

confidence: 84%

“…The L 2 ‐error versus τ , convergence order and CPU time for different values of ( α , β ) are listed in Table , and errors versus h are given in Table . From these tables, it can be found that our approach can achieve higher convergence order with less grid points and shorter CPU time, relative to the method in Ji et al . This advantage is more obvious when dealing with high‐dimensional problems.…”

Section: Resultsmentioning

confidence: 99%

“…In order to further illustrate the superiority of our approach, we employ the numerical method given in Ji et al to make a comparison. In the method of Ji et al the time and space step size are defined by τ = T / M and h = L / N , where M and N are the numbers of temporal and spatial grid points, respectively. The L 2 ‐error versus τ , convergence order and CPU time for different values of ( α , β ) are listed in Table , and errors versus h are given in Table .…”

Section: Resultsmentioning

confidence: 99%

“…The numerical examples for both direct problem and parameter estimation are provided. Particularly, in the numerical simulation of direct problem, we make a comparison between our approach and another method . The numerical results shows that our approach can achieve higher convergence order with less grid points and shorter CPU time.…”

Section: Discussionmentioning

confidence: 99%

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Efficient and accurate spectral method for the time‐fractional dual‐phase‐lag heat transfer model and its parameter estimation

Zheng

Jiang

Zhang

2019

Math Methods in App Sciences

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In the current paper, a heat transfer model is suggested based on a time‐fractional dual‐phase‐lag (DPL) model. We discuss the model in two parts, the direct problem and the inverse problem. Firstly, for solving it, the finite difference/Legendre spectral method is constructed. In the temporal direction, we employ the weighted and shifted Grünwald approximation, which can achieve second order convergence. In the spatial direction, the Legendre spectral method is used, it can obtain spectral accuracy. The stability and convergence are theoretically analyzed. For the inverse problem, the Bayesian method is used to construct an algorithm to estimate the four parameters for the model, namely, the time‐fractional order α, the time‐fractional order β, the delay time τT, and the relaxation time τq. Next, numerical experiments are provided to demonstrate the effectiveness of our scheme, with the values of τq and τT for processed meat employed. We also make a comparison with another method. The data obtained for the direct problem are used in the parameter estimation. The paper provides an accurate and efficient numerical method for the time‐fractional DPL model.

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Section: Discussionmentioning

confidence: 85%

Section: Numerical Examplesmentioning

confidence: 84%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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