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

Authors

  • Dingwen Deng,

    1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
    2. College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, People's Republic of China
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  • Chengjian Zhang

    Corresponding author
    1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
    • School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
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Abstract

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

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