A Multistep Legendre Pseudo-Spectral Method for Nonlinear Volterra Integral Equations

摘要

In this paper, we extend the single-step pseudospectral method for nonlinear 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 the result shows 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 the theoretical expectations.