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Optimized Finite Difference Formulas for Accurate High Frequency Components

Author

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  • Manuel Kindelan
  • Miguel Moscoso
  • Pedro Gonzalez-Rodriguez

Abstract

We present a method to obtain optimal finite difference formulas which maximize their frequency range of validity. The optimization is based on the idea of keeping an error of interest (dispersion, phase, or group velocities errors) below a given threshold for a wavenumber interval as large as possible. To find the weights of these optimal finite difference formulas we solve a system of nonlinear equations. Furthermore, we give compact formulas for the optimal weights as function of the error bound. Several numerical experiments illustrate the performance of the obtained finite difference formulas compared to the standard ones.

Suggested Citation

  • Manuel Kindelan & Miguel Moscoso & Pedro Gonzalez-Rodriguez, 2016. "Optimized Finite Difference Formulas for Accurate High Frequency Components," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-15, December.
    • Handle: RePEc:hin:jnlmpe:7860618
    DOI: 10.1155/2016/7860618
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