A SECOND-ORDER ITERATIVE ALGORITHM FOR A NONLINEAR WAVE EQUATION WITH A NONLOCAL TERM

Abstract

This paper investigates the Dirichlet problem for a nonlinear wave equation involving a nonlinear viscoelastic term and a nonlocal term. By employing a Taylor expansion, a second-order iterative algorithm is constructed. It is proved that the algorithm converges and achieves second-order error estimates.