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Analysis of a fourth-order compact ADI method for a linear hyperbolic equation with three spatial variables

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Abstract

This paper is concerned with a three-level alternating direction implicit (ADI) method for the numerical solution of a 3D hyperbolic equation. Stability criterion of this ADI method is given by using von Neumann method. Meanwhile, it is shown by a discrete energy method that it can achieve fourth-order accuracy in both time and space with respect to H 1- and L 2-norms only if stable condition is satisfied. It only needs solution of a tri-diagonal system at each time step, which can be solved by multiple applications of one-dimensional tri-diagonal algorithm. Numerical experiments confirming the high accuracy and efficiency of the new algorithm are provided.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Dingwen Deng & Chengjian Zhang

  2. College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, 330063, People’s Republic of China

    Dingwen Deng

Authors
  1. Dingwen Deng
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  2. Chengjian Zhang
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Correspondence to Chengjian Zhang.

Additional information

This work is supported by NSFC (Nos. 11171125, 91130003), HSF ( No. 2011CDB289) and SRF of NHU (No. Ec200907255).

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Deng, D., Zhang, C. Analysis of a fourth-order compact ADI method for a linear hyperbolic equation with three spatial variables. Numer Algor 63, 1–26 (2013). https://doi.org/10.1007/s11075-012-9604-8

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  • DOI: https://doi.org/10.1007/s11075-012-9604-8

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