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

摘要

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(2,3). The exact solution is represented in the form of series. The n-term approximation un(t, x) to exact solution u(t, x) is proved to converge to the exact solution. Moreover, the approximate error of un(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.