An Improved Numerical Solution of Burgers' Equation by Cubic B-spline Quasi-interpolation

摘要

In this paper, an improved numerical solution of the Burgers' equation is presented based on the cubic B-spline quasi-interpolation and the compact finite difference method. At first the cubic B-spline quasi-interpolation and the compact finite difference method are introduced. Moreover, the numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative and a two-order compact scheme to approximate the time derivative. The accuracy of our scheme is demonstrated by two problems. The advantage of the resulting scheme is simple with better accuracy, so it is easy to implement. The improved solution could be significant to the applications such as modeling of gas dynamics and traffic flow.