 Gradient preserved method for solving heat conduction equation with variable coefficients in double layersAniruddha Bora and Weizhong Dai Applied Mathematics and Computation, 2020, vol. 386, issue C Abstract: Recently, we have developed an accurate compact finite difference scheme called the Gradient Preserved Method (GPM) for solving heat conduction equation with constant coefficients in double layers. Since functionally graded materials are becoming paramount than materials having uniform structures with the development of new materials, this article extends the GPM to the case where coefficients are variable (and even temperature-dependent). The higher-order compact finite scheme is obtained based on three grid points and is proved to be unconditionally stable and convergent with O(τ2+h4), where τ and h are the time step and grid size, respectively. Numerical errors and convergence orders are tested in an example. Finally, we apply the scheme for predicting electron and lattice temperatures of a gold thin film padding on a chromium film exposed to the ultrashort-pulsed laser. Keywords: Heat conduction equation; Variable coefficient; Multi layer structure; Interface; Stability; Compact finite difference; Convergence; Ultrashort-pulsed laser; Parabolic two step heat equation; Anisotropic diffusion (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304744 DOI: 10.1016/j.amc.2020.125516 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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