Modified Legendre rational spectral method for the Burgers equation on the half-line

Abstract

In this paper, a modified Legendre rational method is discussed for the Burgers equation on the half infinite interval. A fully discrete spectral approximation scheme which possesses the essential conservation properties is established. The stability and the convergence of the discrete scheme are proved by the prior estimate and the error estimate, respectively.

Keywords:

• Burgers’ equation
• Conservation property
• Convergence
• Modified Legendre rational spectral method
• Stability

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.: 10432010 and 10571010). The SI is Professor Lu.