A new fourth-order numerical algorithm for a class of three-dimensional nonlinear evolution equations.

In this article, a new compact alternating direction implicit finite difference scheme is derived for solving a class of 3-D nonlinear evolution equations. By the discrete energy method, it is shown that the new difference scheme has good stability and can attain second-order accuracy in time and fourth-order accuracy in space with respect to the discrete H1 -norm. A Richardson extrapolation algorithm is applied to achieve fourth-order accuracy in temporal dimension. Numerical experiments illustrate the accuracy and efficiency of the extrapolation algorithm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 [ABSTRACT FROM AUTHOR]