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 - <p style="text-align: justify;">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.</p>