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Accurate gradient preserved method for solving heat conduction equations in double layers

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  • Yan, Yun
  • Dai, Weizhong
  • Wu, Longyuan
  • Zhai, Shuying

Abstract

Analyzing heat transfer in layered structures is important for the design and operation of devices and the optimization of thermal processing of materials. Existing numerical methods dealing with layered structures if using only three grid points across the interface usually provide only a second-order truncation error. Obtaining a numerical scheme using three grid points across the interface so that the overall numerical scheme is unconditionally stable and convergent with higher-order accuracy is mathematically challenging. In this study, we develop a higher-order accurate finite difference method using three grid points across the interface by preserving the first-order derivative, ux, in the interfacial condition and/or the boundary condition. As such, when the compact fourth-order accurate Padé scheme is used at the interior points, the overall scheme maintains to be higher-order accurate. Stability and convergence of the scheme are analyzed. Finally, four examples are given to test the obtained numerical method. Results show that the convergence order in space is close to 4.0, which coincides with the theoretical analysis.

Suggested Citation

  • Yan, Yun & Dai, Weizhong & Wu, Longyuan & Zhai, Shuying, 2019. "Accurate gradient preserved method for solving heat conduction equations in double layers," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 58-85.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:58-85
    DOI: 10.1016/j.amc.2019.02.038
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    Citations

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    Cited by:

    1. Bora, Aniruddha & Dai, Weizhong, 2020. "Gradient preserved method for solving heat conduction equation with variable coefficients in double layers," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    2. Chinonso I. Nwankwo & Weizhong Dai & Ruihua Liu, 2023. "Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 817-854, October.
    3. Chinonso Nwankwo & Weizhong Dai & Ruihua Liu, 2019. "Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model," Papers 1908.04900, arXiv.org, revised Jun 2020.
    4. Chinonso Nwankwo & Weizhong Dai & Tony Ware, 2023. "Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping," Papers 2309.03984, arXiv.org, revised Sep 2023.
    5. Chinonso Nwankwo & Weizhong Dai, 2020. "Multigrid Iterative Algorithm based on Compact Finite Difference Schemes and Hermite interpolation for Solving Regime Switching American Options," Papers 2008.00925, arXiv.org, revised Nov 2021.

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