@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} }