Abstract

In this paper, we construct and suggest some new, efficient, and accurate numerical algorithms based on the spectral methods for solving the Burgers’ equation. Spectral methods using Chebyshev and Legendre polynomials are developed. Test problems are used to validate these methods that are found to be accurate and efficient. Also, the results show that despite the fact that Chebyshev polynomials are the most widely used ones; the use of Legendre polynomials gives more accurate results. In addition the present study includes numerical solution of Burgers’ equation by means of the Adomian decomposition method. Comparison with other methods is also given.

Key words: Burgers’ equation, spectral, Adomian, Tanh methods.