TY - JOUR
T1 - Chebyshev Spectral Method for Volterra Integral Equation with Multiple Delays
AU - Zheng , Weishan
AU - Chen , Yanping
JO - Journal of Mathematical Study
VL - 2
SP - 214
EP - 226
PY - 2018
DA - 2018/06
SN - 51
DO - http://doi.org/10.4208/jms.v51n2.18.06
UR - https://global-sci.org/intro/article_detail/jms/12464.html
KW - Volterra integral equation, multiple delays, Chebyshev spectral method, Gronwall inequality, convergence analysis.
AB - <p style="text-align: justify;">Numerical analysis is carried out for the Volterra integral equation with
multiple delays in this article. Firstly, we make two variable transformations. Then
we use the Gauss quadrature formula to get the approximate solutions. And then with
the Chebyshev spectral method, the Gronwall inequality and some relevant lemmas,
a rigorous analysis is provided. The conclusion is that the numerical error decay exponentially
in $L^∞$ space and $L^2_{ω^c}$ space. Finally, numerical examples are given to show
the feasibility and effectiveness of the Chebyshev spectral method.</p>