An efficient high-order compact finite difference scheme based on proper orthogonal decomposition for the multi-dimensional parabolic equation
作者: Baozou XuXiaohua Zhang
作者单位: 1College of Science, China Three Gorges University
2Three Gorges Mathematical Research Center, China Three Gorges University
刊名: Advances in Difference Equations, 2019, Vol.2019 (1), pp.1-22
来源数据库: Springer Nature Journal
DOI: 10.1186/s13662-019-2273-3
关键词: Compact finite difference schemeProper orthogonal decompositionMulti-dimensional parabolic equationStrang splitting method
英文摘要: Abstract(#br)In this paper, the combination of efficient sixth-order compact finite difference scheme (E-CFDS6) based proper orthogonal decomposition and Strang splitting method (E-CFDS6-SSM) is constructed for the numerical solution of the multi-dimensional parabolic equation (MDPE). For this purpose, we first develop the CFDS6 to attain a high accuracy for the one-dimensional parabolic equation (ODPE). Then, by the Strang splitting method, we have converted the MDPE into a series of one-dimensional ODPEs successfully, which is easier to implement and program with CFDS6 than an alternating direction implicit method. Finally, we employ proper orthogonal decomposition techniques to improve the computational efficiency of CFDS6 and build the E-CFDS6-SSM with fewer unknowns and sufficiently...
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影响因子:0.76 (2012)

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