Sobolev orthogonal Legendre rational spectral methods for problems on the half line

Abstract

Modified Legendre rational spectral methods for solving second‐order differential equations on the half line are proposed. Some Sobolev orthogonal Legendre rational basis functions are constructed, which lead to the diagonalization of discrete systems. Accordingly, both the exact solutions and the approximate solutions can be represented as infinite and truncated Fourier series. Numerical results demonstrate the effectiveness and the spectral accuracy of this approach.