TY - JOUR
T1 - Super Implicit Multistep Collocation Methods for Weakly Singular Volterra Integral Equations
AU - Zhao , Jingjun
AU - Long , Teng
AU - Xu , Yang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1039
EP - 1065
PY - 2019
DA - 2019/06
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2018-0084
UR - https://global-sci.org/intro/article_detail/nmtma/13214.html
KW - Collocation method, Volterra integral equation, weakly singular kernel, convergence.
AB - <p style="text-align: justify;">In this paper, we consider super implicit multistep collocation methods for solving weakly singular Volterra integral equations. After the integral equations are regularized by smoothing transformations, super implicit multistep collocation methods are constructed. Convergence and the linear stability of these methods are analyzed. The theoretical result is also demonstrated by numerical examples.</p>