In this paper, a general framework is presented for analyzing numerical methods for the evolutionary equations that admit semigroup formulations. This framework is then applied to spectral and pseudospectral methods for the Burgers' equation, using trigonometric, Chebyshev, and Legendre polynomials. Optimal order of convergence is obtained, which implies the spectral accuracy of these methods.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics