TY - JOUR
T1 - Fully Diagonalized Chebyshev Spectral Methods for Second and Fourth Order Elliptic Boundary Value Problems
AU - Li , Jing-Min
AU - Wang , Zhong-Qing
AU - Li , Huiyuan
JO - International Journal of Numerical Analysis and Modeling
VL - 1-2
SP - 243
EP - 259
PY - 2018
DA - 2018/01
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10566.html
KW - Spectral method, biorthogonal Chebyshev polynomials, elliptic boundary value problems, numerical results.
AB - <p style="text-align: justify;">Fully diagonalized Chebyshev spectral methods for solving second and fourth order elliptic boundary value problems are proposed. They are based on appropriate base functions for the Galerkin formulations which are complete and biorthogonal with respect to certain Sobolev inner product. The suggested base functions lead to 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.</p>