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Why we use finite number of Terms in Fourier Decomposition of Error in Von Neumann St |
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January 26, 2018, 09:17 |
Why we use finite number of Terms in Fourier Decomposition of Error in Von Neumann St
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#1 |
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abcd efgh ijkl
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In Fourier decomposition of error in Von Neumann stability analysis, we assume that the domain is of finite length, and therefore, we use discrete Fourier representation. My question is why we use finite number of harmonics instead of infinite number of harmonics?
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January 26, 2018, 10:42 |
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#2 | |
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Filippo Maria Denaro
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The answer is twofold. 1) the finite lenght L, once subdivided by a finite number of N step of size h, introduces the Nyquist cut-off frequency Kc=L/2h. No Fourier components are represented beyond Kc. 2) The von Neumann analysis is linear, therefore we introduce one generic components having wavenumber ranging from the lowest to the highest represented. |
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January 26, 2018, 14:46 |
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#3 | |
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abcd efgh ijkl
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stability analysis, von neumann |
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