Optimized Finite Difference Formulas for Accurate High Frequency Components

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 possi...

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Bibliographic Details
Published in:Mathematical problems in engineering 2016-01, Vol.2016 (2016), p.1-15
Main Authors: Kindelan, Manuel, Gonzalez-Rodriguez, Pedro, Moscoso, Miguel
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Engineering
Errors
Finite difference method
Formulas (mathematics)
Frequency ranges
High frequencies
Mathematical analysis
Mathematical models
Methods
Nonlinear equations
Optimization
Velocity
Wavelengths
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Summary: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.
ISSN:1024-123X
1563-5147
DOI:10.1155/2016/7860618