Fourierization of the Legendre--Galerkin method and a new space--time spectral method

Authors:
Jie Shen;Li-Lian Wang
Affiliations:
Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA;Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, 637616 Singapore
Venue:
Applied Numerical Mathematics
Year:
2007

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Abstract

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.