A novel finite difference scheme for Burgers' equation on unbounded domains

作者：Zheng, Quan^*; Zhao, Xin; Liu, Yufeng

来源：Applied Numerical Mathematics, 2017, 111: 1-16.

DOI：10.1016/j.apnum.2016.09.002

• Nonhomogeneous Burgers' equation
• Unbounded domain
• Artificial boundary condition
• Finite difference method
• Error estimate

This paper studies a finite difference method for one-dimensional nonhomogeneous Burgers' equation on the infinite domain. Two exact nonlinear artificial boundary conditions are applied on two artificial boundaries to limit the original problem onto a bounded computational domain. A function transformation makes both Burgers' equation and artificial boundary conditions linear. Consequently, a novel finite difference scheme is developed by using the method of reduction of order for the obtained equation and artificial boundary conditions. The stability and the convergence with order 3/2 in time and 2 in space in an energy norm are proved for this method for Burgers' equation. Different examples illustrate the unconditional stability and the accuracy of the proposed method.

• 出版日期2017-1
• 单位北方工业大学