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 ( Δ t 2 + h x 4 + h y 4 ) in H 1 - and L ∞ -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.