TY - JOUR
T1 - Convergence Analysis of Legendre-Collocation Spectral Methods for Second Order Volterra Integro-Differential Equation with Delay
AU - Zheng , Weishan
AU - Chen , Yanping
AU - Huang , Yunqing
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 486
EP - 500
PY - 2019
DA - 2019/01
SN - 11
DO - http://doi.org/10.4208/aamm.OA-2018-0121
UR - https://global-sci.org/intro/article_detail/aamm/12973.html
KW - Convergence analysis, Legendre-spectral method, second
order Volterra integro-differential equation, delay, error analysis.
AB - <p style="text-align: justify;">In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both $L^{2}$-norm and $L^{\infty}$-norm. In the end, the numerical experiment is illustrated to confirm the theoretical analysis.</p>