Convergence Analysis of Legendre-Collocation Spectral Methods for Second Order Volterra Integro-Differential Equation with Delay (Advances in Applied Mathematics and Mechanics, 2019)
In this paper, a Legendre-collocation spectral method is developed for the second order Volterra integro-differential equation with delay. We provide a rigorous error analysis for the proposed method. The spectral rate of convergence for the proposed method is established in both $L^{2}$-norm and $L^{∞}$-norm. In the end, the numerical experiment is illustrated to confirm the theoretical analysis.