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Volume 53, Issue 2
High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods

Sheng Chen

DOI: 10.4208/jms.v53n2.20.02

J. Math. Study, 53 (2020), pp. 143-158.

Published online: 2020-05

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  • Abstract

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.

  • Keywords

Singularly perturbed problems, weakly singular integral equations, boundary layers, enriched spectral Galerkin methods, Jacobi polynomials.

  • AMS Subject Headings

65N35, 65R20, 41A30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

shengchen@jsnu.edu.cn (Sheng Chen)

  • BibTex
  • RIS
  • TXT
@Article{JMS-53-143, author = {Chen , Sheng}, title = {High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods}, journal = {Journal of Mathematical Study}, year = {2020}, volume = {53}, number = {2}, pages = {143--158}, abstract = {

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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v53n2.20.02}, url = {http://global-sci.org/intro/article_detail/jms/16802.html} }
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 -

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.

Sheng Chen. (2020). High-Accuracy Numerical Approximations to Several Singularly Perturbed Problems and Singular Integral Equations by Enriched Spectral Galerkin Methods. Journal of Mathematical Study. 53 (2). 143-158. doi:10.4208/jms.v53n2.20.02
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