TY - JOUR
T1 - High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods
AU - Chen , Sheng
JO - Journal of Mathematical Study
VL - 2
SP - 143
EP - 158
PY - 2020
DA - 2020/05
SN - 53
DO - http://doi.org/10.4208/jms.v53n2.20.02
UR - https://global-sci.org/intro/article_detail/jms/16802.html
KW - Singularly perturbed problems, weakly singular integral equations, boundary layers, enriched spectral Galerkin methods, Jacobi polynomials.
AB - <p style="text-align: justify;">Usual spectral methods are not effective for singularly perturbed problems
and singular integral equations due to the boundary layer functions or weakly singular solutions. To overcome this difficulty, the enriched spectral-Galerkin methods
(ESG) are applied to deal with a class of singularly perturbed problems and singular
integral equations for which the form of leading singular solutions can be determined.
In particular, for easily understanding the technique of ESG, the detail of the process
are provided in solving singularly perturbed problems. Ample numerical examples
verify the efficiency and accuracy of the enriched spectral Galerkin methods.</p>