Chebyshev Spectral Method for Volterra Integral Equation with Multiple Delays (Journal of Mathematical Study, 2018)
Numerical analysis is carried out for the Volterra integral equation withmultiple delays in this article. Firstly, we make two variable transformations. Thenwe use the Gauss quadrature formula to get the approximate solutions. And then withthe Chebyshev spectral method, the Gronwall inequality and some relevant lemmas,a rigorous analysis is provided. The conclusion is that the numerical error decay exponentiallyin $L^∞$ space and $L^2_{ω^c}$ space. Finally, numerical examples are given to showthe feasibility and effectiveness of the Chebyshev spectral method.