TY - JOUR
T1 - Piecewise Spectral Collocation Method for Second Order Volterra Integro-Differential Equations with Nonvanishing Delay
AU - Chen , Zhenrong
AU - Chen , Yanping
AU - Huang , Yunqing
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1333
EP - 1356
PY - 2022
DA - 2022/08
SN - 14
DO - http://doi.org/10.4208/aamm.OA-2021-0334
UR - https://global-sci.org/intro/article_detail/aamm/20850.html
KW - Second-order Volterra type integro-differential equation, delay function, piecewise spectral-collocation method.
AB - <p style="text-align: justify;">In this paper, the piecewise spectral-collocation method is used to solve the
second-order Volterra integral differential equation with nonvanishing delay. In this
collocation method, the main discontinuity point of the solution of the equation is
used to divide the partitions to overcome the disturbance of the numerical error convergence caused by the main discontinuity of the solution of the equation. Derivative
approximation in the sense of integral is constructed in numerical format, and the convergence of the spectral collocation method in the sense of the $L^∞$ and $L^2$ norm is
proved by the Dirichlet formula. At the same time, the error convergence also meets
the effect of spectral accuracy convergence. The numerical experimental results are
given at the end also verify the correctness of the theoretically proven results.</p>