Numerical Analysis for Cubic Delay Integral Equation

Numerical analysis is proposed for the integral equation with cubic delay in this article. Firstly, make two linear variable transformation. Then use the Gauss quadrature formula to get the approximate solution. And then with the Chebyshev spectral-collocation method、the Gronwall inequality and some other lemmas, a rigorous analysis is provided. The conclusion is that the numerical error decay exponentially in the L^{\infty}space and L^2_{\omega^c} space. In the end, numerical example is given to show the feasibility and effectiveness of the Chebyshev spectral collocation method.