A multistep Legendre pseudo-spectral method for Volterra integral equations

摘要

In this paper, we extend the single-step pseudo-spectral method for Volterra integral equations of the second kind to the multistep pseudo-spectral method. We also analyze the convergence of the hp-version of the multistep pseudo-spectral method under the L-2-norm, and show that the scheme enjoys high order accuracy and can be implemented in a stable and efficient manner. In addition, it is very suitable for long time calculations and large step size situations. Numerical experiments confirm theoretical expectations. (C) 2015 Elsevier Inc. All rights reserved.