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Note on a Fourth Order Finite Difference Scheme for the Wave Equation

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Abstract

The linear wave equation is one of the simplest partial differential equations. It has been used as a test equation of hyperbolic systems for different numerical schemes [Richtmyer and Morton (1967); Euvrard (1994); and Lax (1990]. In this short note, a Fourth order finite difference scheme for this equation is proposed and studied. Numerical simulations confirm our theoretical analyses of accuracy and stability condition. It will be interesting to extend the scheme to nonlinear hyperbolic systems.

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REFERENCES

  • Chu, C. K. (1984). An Introduction to Computational Fluid Dynamics, Science Press, Beijing.

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  • Euvrard, D. (1994). Résolution Numérique des Equations aux Dérivées Partielles, Masson, Paris.

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  • Lax, P. (1990). Hyperbolic systems of conservative laws and the mathematical theory of shock waves. SIAM, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 11.

  • Richtmyer, R. D., and Morton, K. W. (1967). Difference Methods for Initial-Value Problems, Second Edition, John Wiley, New York.

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Authors and Affiliations

  1. Department of Applied Physics and Applied Math, Columbia University, New York, New York, 10027

    Yuehong Qian

  2. Department of Electric Engineering, Columbia University, New York, New York, 10027

    Jose Jimenez

Authors
  1. Yuehong Qian
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  2. Jose Jimenez
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Qian, Y., Jimenez, J. Note on a Fourth Order Finite Difference Scheme for the Wave Equation. Journal of Scientific Computing 13, 461–469 (1998). https://doi.org/10.1023/A:1023241418582

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  • DOI: https://doi.org/10.1023/A:1023241418582

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