TY - JOUR
T1 - A Diagonalized Legendre Rational Spectral Method for Problems on the Whole Line
AU - Yu , Xuhong
AU - Zhao , Yunge
AU - Wang , Zhongqing
JO - Journal of Mathematical Study
VL - 2
SP - 196
EP - 213
PY - 2018
DA - 2018/06
SN - 51
DO - http://doi.org/10.4208/jms.v51n2.18.05
UR - https://global-sci.org/intro/article_detail/jms/12463.html
KW - Legendre rational spectral method, Sobolev orthogonal functions, elliptic boundary value problems, heat equation, numerical results.
AB - <p style="text-align: justify;">A diagonalized Legendre rational spectral method for solving second and
fourth order differential equations are proposed. Some Fourier-like Sobolev orthogonal
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 of this approach.</p>