Difference between revisions of "Numerical Differentiation"
From Sutherland_wiki
m (NumericalDifferentiation moved to Numerical Differentiation) |
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| Backward Difference | | Backward Difference | ||
− | | <math> \left. \frac{\mathrm{d}}{\mathrm{d}x} \right|_{i} \approx \frac{\phi_{i}-\phi_{i-1}}{\Delta x}</math> | + | | <math> \left. \frac{\mathrm{d}\phi}{\mathrm{d}x} \right|_{i} \approx \frac{\phi_{i}-\phi_{i-1}}{\Delta x}</math> |
| <math>\mathcal{O}\left(\Delta x \right) </math> | | <math>\mathcal{O}\left(\Delta x \right) </math> | ||
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| Central Difference | | Central Difference | ||
− | | | <math> \left. \frac{\mathrm{d}}{\mathrm{d}x} \right|_{i | + | | | <math> \left. \frac{\mathrm{d\phi}}{\mathrm{d}x} \right|_{i} \approx \frac{\phi_{i+1}-\phi_{i-1}}{2\Delta x}</math> |
| <math>\mathcal{O}\left(\Delta x^2 \right) </math> | | <math>\mathcal{O}\left(\Delta x^2 \right) </math> | ||
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Revision as of 09:24, 7 July 2008
Contents
Introduction
Taylor Series
Lagrange Polynomials
Lagrange polynomials, which are commonly used for interpolation, can also be used for differentiation.
Tables for Derivatives on Uniform Grids
Derivative at point | Discrete Representation (uniform mesh) | Order |
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Forward Difference | ||
Backward Difference | ||
Central Difference |
Derivative at point | Discrete Representation (uniform mesh) | Order |
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