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標題: Tailored finite point method for solving one-dimensional Burgers' equation
作者: Tsai, Chih-Ching
Shih, Yin-Tzer
Lin, Yu-Tuan
Wang, Hui-Ching
關鍵字: Burgers' equation;Tailored finite point;Hopf–Cole transformation;viscous flows;explicit scheme
Project: International Journal of Computer Mathematics, Volume 94, 2017 - Issue 4
We propose a tailored finite point method (TFPM) for solving a quasilinear time-dependent Burgers' equation with a small coefficient of viscosity. The selected basis functions for the TFPM automatically fit the properties of the local solution in time and space simultaneously. The stability and error analysis for the TFPM are given. We also demonstrate the efficiency of the proposed scheme on relatively coarse meshes. The numerical results indicate that the TFPM achieves high accuracy and effectively captures the shock solutions.
DOI: 10.1080/00207160.2016.1148812
Appears in Collections:應用數學系所

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