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Tailored Finite Point Method for First Order Wave Equation

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Abstract

Following the idea of the tailored finite point method proposed in Han and Huang (J. Comput. Math. 26:728–739, 2008) and Huang (Netw. Heterog. Media 4:91–106, 2009), a series of efficient numerical schemes are developed for the one dimensional scalar wave equation within various types of media. Stability and accuracy are analyzed and numerically verified. In particular we can obtain unconditionally stable implicit schemes that can be solved explicitly for boundary value problems. We can also deal with the propagation of discontinuity and highly oscillatory waves efficiently. The generalization to higher order schemes is straightforward.

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Author notes

  1. Xu Yang

    Present address: Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Zhongyi Huang

  2. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Xu Yang

Authors
  1. Zhongyi Huang
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  2. Xu Yang
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Corresponding author

Correspondence to Zhongyi Huang.

Additional information

This work was partially supported by NSFC project No. 11071139, the National Basic Research Program of China under the grant 2011CB309705, Tsinghua University Initiative Scientific Research Program. This work was done during X.Y.’s visit to Tsinghua University, and he is grateful to their hospitality.

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Huang, Z., Yang, X. Tailored Finite Point Method for First Order Wave Equation. J Sci Comput 49, 351–366 (2011). https://doi.org/10.1007/s10915-011-9468-4

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  • DOI: https://doi.org/10.1007/s10915-011-9468-4

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