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A compact finite difference method for solving Burgers' equation
Author(s) -
Xie Shusen,
Li Guangxing,
Yi Sucheol,
Heo Sunyeong
Publication year - 2009
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2041
Subject(s) - burgers' equation , mathematics , compact finite difference , convergence (economics) , transformation (genetics) , stability (learning theory) , finite difference method , space (punctuation) , finite difference , scheme (mathematics) , order (exchange) , mathematical analysis , order of accuracy , numerical analysis , numerical stability , partial differential equation , computer science , biochemistry , chemistry , finance , machine learning , economics , gene , economic growth , operating system
In this paper, a high‐order accurate compact finite difference method using the Hopf–Cole transformation is introduced for solving one‐dimensional Burgers' equation numerically. The stability and convergence analyses for the proposed method are given, and this method is shown to be unconditionally stable. To demonstrate efficiency, numerical results obtained by the proposed scheme are compared with the exact solutions and the results obtained by some other methods. The proposed method is second‐ and fourth‐order accurate in time and space, respectively. Copyright © 2009 John Wiley & Sons, Ltd.