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.