Piecewise Spectral Collocation Method for Second Order Volterra Integro-Differential Equations with Nonvanishing Delay (Advances in Applied Mathematics and Mechanics, 2022)
In this paper, the piecewise spectral-collocation method is used to solve thesecond-order Volterra integral differential equation with nonvanishing delay. In thiscollocation method, the main discontinuity point of the solution of the equation isused to divide the partitions to overcome the disturbance of the numerical error convergence caused by the main discontinuity of the solution of the equation. Derivativeapproximation in the sense of integral is constructed in numerical format, and the convergence of the spectral collocation method in the sense of the $L^∞$ and $L^2$ norm isproved by the Dirichlet formula. At the same time, the error convergence also meetsthe effect of spectral accuracy convergence. The numerical experimental results aregiven at the end also verify the correctness of the theoretically proven results.