A new fourth-order numerical algorithm for a class of nonlinear wave equations

In this paper, a new three-level compact alternating direction implicit (ADI) difference scheme is derived for solving a kind of nonlinear wave equations. Basing on a fourth-order approximation to the exact solution at the first time level, it is shown by the energy method that the numerical solution is conditionally convergent with an order of O(Delta t(2) + h(x)(4) + h(y)(4)) in H-1- and L-infinity-norms. A new Richardson extrapolation formula based on three time-grid parameters is given to get numerical solution of fourth-order accuracy in both time and space. The performance of the new algorithm is illustrated by numerical experiments. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.