A computational method for solving one-dimensional variable-coefficient Burgers equation

作者：Cui Minggen^*; Geng Fazhan

来源：Applied Mathematics and Computation, 2007, 188(2): 1389-1401.

DOI：10.1016/j.amc.2006.11.005

• exact solution
• variable-coefficient Burgers equation
• reproducing kernel

The Burgers equation is a simple one-dimensional model of the Navier-Stoke equation. In this paper, the exact solution to one-dimensional variable-coefficient Burgers equation is obtained in the reproducing kernel space W-(2,W-3). The exact solution is represented in the form of series. The n-term approximation u(n)(t, x) to exact solution u(t, x) is proved to converge to the exact solution. Moreover, the approximate error of u(n)(t, x) is monotone decreasing. Some numerical examples have been studied to demonstrate the accuracy of the present method. Results obtained by the method have been compared with the exact solution of each example and are found to be in good agreement with each other.

• 出版日期2007-5-15
• 单位哈尔滨工业大学