A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line (Journal of Mathematical Study, 2018)
A diagonalized Legendre rational spectral method for solving second andfourth order differential equations are proposed. Some Fourier-like Sobolev orthogonalbasis functions are constructed which lead to the diagonalization of discrete systems.Accordingly, both the exact solutions and the approximate solutions can be representedas infinite and truncated Fourier series. Numerical results demonstrate theeffectiveness of this approach.
Keywords: Legendre rational spectral method; Sobolev orthogonal functions; elliptic boundary value problems; heat equation; numerical results.