Optimized Finite Difference Formulas for Accurate High Frequency Components Articles uri icon

publication date

  • December 2016

issue

  • Article ID 7860618

volume

  • 2016

international standard serial number (ISSN)

  • 1024-123X

electronic international standard serial number (EISSN)

  • 1563-5147

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.