Resumen de Fourierization of the Legendre¿Galerkin method and a new space¿time spectral method

Jie Shen, Li-Lian Wang

• A set of Fourier-like basis functions is constructed for Legendre¿Galerkin method for non-periodic boundary value problems and a new space¿time spectral method is proposed. A complete error analysis is carried out for a linear parabolic equation and numerical results are presented for several typical linear and nonlinear equations.