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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 = {Can Huang, Tao Tang and Zhimin Zhang}, 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 AU - Can Huang, Tao Tang & Zhimin Zhang 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 and Zhimin Zhang. (2011). 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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