TY - JOUR
T1 - Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations
AU - Yang , Yin
AU - Chen , Yanping
AU - Huang , Yunqing
AU - Yang , Wei
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 74
EP - 88
PY - 2018
DA - 2018/03
SN - 7
DO - http://doi.org/10.4208/aamm.2013.m163
UR - https://global-sci.org/intro/article_detail/aamm/10945.html
KW - 
AB - <p style="text-align: justify;">A Legendre-collocation method is proposed to solve the nonlinear
Volterra integral equations of the second kind. We provide a
rigorous error analysis for the proposed method, which indicates that
the numerical errors in $L^2$-norm and &nbsp;$L^\infty$-norm will decay
exponentially provided that the kernel function is sufficiently
smooth. Numerical results are presented, which confirm the
theoretical prediction of the exponential rate of convergence.</p>