A spectrally accurate time - space pseudospectral method for viscous Burgers' equation

The aim of the paper is to develop and analyze a spectrally accurate pseudospectral method in time and space to find the approximate solution of the viscous Burgers' equation. The method is employed in time and space both at Chebyshev- Gauss- Lobbato (CGL) points. The approximate solution is represented in terms of basis functions. The spectral coefficients are found in such a way that the residual becomes minimum. The given problem is reduced to a system of nonlinear algebraic equations, which is solved by Newton-Raphson's method. Error estimates for interpolating polynomials are derived. The computational experiments are carried out to corroborate the theoretical results and to compare the present method with existing methods in the literature.