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An Artificial Boundary Method for Burgers’ Equation in the Unbounded Domain

Quan Zheng1,2, Lei Fan1, Xuezheng Li1
College of Sciences, North China University of Technology, Beijing 100144, China.

Computer Modeling in Engineering & Sciences 2014, 100(6), 445-461.


In this paper, we construct a numerical method for one-dimensional Burgers’ equation in the unbounded domain by using artificial boundary conditions. The original problem is converted by Hopf-Cole transformation to the heat equation in the unbounded domain, the latter is reduced to an equivalent problem in a bounded computational domain by using two artificial integral boundary conditions, a finite difference method with discrete artificial boundary conditions is established by using the method of reduction of order for the last problem, and thereupon the numerical solution of Burgers’ equation is obtained. This artificial boundary method is proved and verified to be uniquely solvable, unconditionally stable and convergent with the order 2 in space and the order 3/2 in time for solving Burgers’ equation on the computational domain.


Burgers’ equation, Unbounded domain, Hopf-Cole transformation, Artificial boundary method, Finite difference method

Cite This Article

Zheng, Q., Fan, L., Li, X. (2014). An Artificial Boundary Method for Burgers’ Equation in the Unbounded Domain. CMES-Computer Modeling in Engineering & Sciences, 100(6), 445–461.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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