Tailored finite point method for solving one-dimensional Burgers' equation

被引：8

作者：

Tsai, Chih-Ching ^{[1
]}

Shih, Yin-Tzer ^{[1
]}

Lin, Yu-Tuan ^{[1
,2
]}

Wang, Hui-Ching ^{[1
]}

机构：

[1] Natl Chung Hsing Univ, Dept Appl Math, Taichung, Taiwan

[2] Acad Sinica, Math Inst, Taipei, Taiwan

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2017年 / 94卷 / 04期

关键词：

Burgers' equation; Tailored finite point; Hopf-Cole transformation; viscous flows; explicit scheme; NUMERICAL-SOLUTION; ELEMENT-METHOD; DIFFERENCE;

D O I：

10.1080/00207160.2016.1148812

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：800 / 812

页数：13

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