Piecewise Spectral Collocation Method for Second Order Volterra Integro-Differential Equations with Nonvanishing Delay

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-infinity 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.