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Volume 29, Issue 6
Supergeometric Convergence of Spectral Collocation Methods for Weakly Singular Volterra and Fredholm Integral Equations with Smooth Solutions

Can Huang, Tao Tang & Zhimin Zhang

DOI: 10.4208/jcm.1110-m11si06

J. Comp. Math., 29 (2011), pp. 698-719.

Published online: 2011-12

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  • Abstract

A spectral collocation method is proposed to solve Volterra or Fredholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of functions that satisfy certain regularity conditions on a bounded domain, we obtain geometric or supergeometric convergence rate for both types of equations. Numerical results confirm our theoretical analysis.

  • Keywords

Weakly singular kernel, Integro-differential equations, Collocation method.

  • AMS Subject Headings

45G20, 46A16, 46A22, 65M70.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-29-698, author = {}, title = {Supergeometric Convergence of Spectral Collocation Methods for Weakly Singular Volterra and Fredholm Integral Equations with Smooth Solutions}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {6}, pages = {698--719}, abstract = {

A spectral collocation method is proposed to solve Volterra or Fredholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of functions that satisfy certain regularity conditions on a bounded domain, we obtain geometric or supergeometric convergence rate for both types of equations. Numerical results confirm our theoretical analysis.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1110-m11si06}, url = {http://global-sci.org/intro/article_detail/jcm/8501.html} }
TY - JOUR T1 - Supergeometric Convergence of Spectral Collocation Methods for Weakly Singular Volterra and Fredholm Integral Equations with Smooth Solutions JO - Journal of Computational Mathematics VL - 6 SP - 698 EP - 719 PY - 2011 DA - 2011/12 SN - 29 DO - http://doi.org/10.4208/jcm.1110-m11si06 UR - https://global-sci.org/intro/article_detail/jcm/8501.html KW - Weakly singular kernel, Integro-differential equations, Collocation method. AB -

A spectral collocation method is proposed to solve Volterra or Fredholm integral equations with weakly singular kernels and corresponding integro-differential equations by virtue of some identities. For a class of functions that satisfy certain regularity conditions on a bounded domain, we obtain geometric or supergeometric convergence rate for both types of equations. Numerical results confirm our theoretical analysis.

Can Huang, Tao Tang & Zhimin Zhang. (1970). Supergeometric Convergence of Spectral Collocation Methods for Weakly Singular Volterra and Fredholm Integral Equations with Smooth Solutions. Journal of Computational Mathematics. 29 (6). 698-719. doi:10.4208/jcm.1110-m11si06
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