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

Authors:
Dingwen Deng;Chengjian Zhang
Affiliations:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Peoples Republic of China and College of Mathematics and Information Science, Nanchang Hangkong U ...;School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Peoples Republic of China
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

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(@Dt^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.