Chebyshev Spectral Method for Volterra Integral Equation with Multiple Delays

Abstract

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.