TY - JOUR
T1 - Efficient Implementation of a Spectral-Tau Method for a Class of Two-Point Boundary-Value and Initial-Boundary-Value Problems
AU - Liu , Fei
JO - Journal of Mathematical Study
VL - 2
SP - 190
EP - 207
PY - 2014
DA - 2014/06
SN - 47
DO - http://doi.org/10.4208/jms.v47n2.14.04
UR - https://global-sci.org/intro/article_detail/jms/9954.html
KW - Spectral-tau method, variable coefficients, separable equation, Thomas-Fermi equation.
AB - <p style="text-align: justify;">A simple and efficient spectral method for solving the second, third order and fourth order elliptic equations with variable coefficients and nonlinear differential equations is presented. It is different from spectral-collocation method which leads to dense, ill-conditioned matrices. The spectral method in this paper solves for the coefficients of the solution in a Chebyshev series, leads to discrete systems with special structured matrices which can be factorized and solved efficiently. We also extend the method to boundary value problems in two space dimensions and solve 2-D separable equation with variable coefficients. As an application, we solve Cahn-Hilliard equation iteratively via first-order implicit time discretization scheme. Ample numerical results indicate that the proposed method is extremely accurate and efficient.</p>