AN hp-SPECTRAL COLLOCATION METHOD FOR NONLINEAR VOLTERRA INTEGRAL EQUATIONS WITH VANISHING VARIABLE DELAYS.

In this paper, we propose a multistep Legendre-Gauss spectral collocation method for nonlinear second-kind Volterra integral equations (VIEs) with vanishing variable delays. This method is easy to implement and possesses high-order accuracy. We also provide a rigorous convergence analysis of the hp-version of the multistep spectral collocation method under L2-norm. Numerical results confirm the theoretical predictions. [ABSTRACT FROM AUTHOR]