Optimized Finite Difference Formulas for Accurate High Frequency Components
| Autor: | Manuel Kindelan, Miguel Moscoso, Pedro González-Rodríguez |
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| Přispěvatelé: | Ministerio de Economía y Competitividad (España) |
| Rok vydání: | 2016 |
| Předmět: |
Article Subject
General Mathematics lcsh:Mathematics Mathematical analysis General Engineering Phase (waves) Finite difference Finite difference coefficient 010103 numerical & computational mathematics Interval (mathematics) Function (mathematics) 010502 geochemistry & geophysics lcsh:QA1-939 01 natural sciences Nonlinear system lcsh:TA1-2040 Range (statistics) Wavenumber 0101 mathematics lcsh:Engineering (General). Civil engineering (General) Biología y Biomedicina 0105 earth and related environmental sciences Mathematics |
| Zdroj: | e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid instname e-Archivo: Repositorio Institucional de la Universidad Carlos III de Madrid Universidad Carlos III de Madrid (UC3M) Mathematical Problems in Engineering, Vol 2016 (2016) |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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