TY - JOUR T1 - A Chebyshev Spectral Collocation Method for Nonlinear Volterra Integral Equations with Vanishing Delays JO - East Asian Journal on Applied Mathematics VL - 2 SP - 233 EP - 260 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/eajam.130416.071217a UR - https://global-sci.org/intro/article_detail/eajam/12203.html KW - Multistep Chebyshev-Gauss-Lobatto spectral collocation method, nonlinear Volterra integral equation, vanishing variable delay. AB -

A multistep Chebyshev-Gauss-Lobatto spectral collocation method for nonlinear Volterra integral equations with vanishing delays is developed. The convergence of the hp-version of the method in supremum norm is proved. Numerical experiments show the efficiency of the method for equations with highly oscillating, steep gradient and non-smooth solutions.