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Update clenshaw in website table
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Ali-Tehrani committed Aug 3, 2023
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2 changes: 1 addition & 1 deletion doc/table_onedgrids.csv
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Expand Up @@ -8,6 +8,6 @@ Grid;Domain;:math:`x_i`;:math:`w_i`
:func:`Tanh Sinh<grid.onedgrid.TanhSinh>`;:math:`[-1,1]`;:math:`\tanh\left( \frac{\pi}{2} \sinh(i\delta) \right)`;:math:`\frac{\frac{\pi}{2}\delta \cosh(i\delta)}{\cosh^2(\frac{\pi}{2}\sinh(i\delta))}`
:func:`Simpson<grid.onedgrid.Simpson>`;:math:`[-1,1]`;:math:`-1 + 2 \left(\frac{i-1}{N_{pts}-1}\right)`;:math:`w_i = 2 / (3(N - 1)) \text{ if } i = 0, \quad 8 / (3(N - 1)) \text{ if } i \geq 1 \text{ and is odd}, \quad 4 / (3(N - 1)) \text{ if } i \geq 2 \text{ and is even}.`
:func:`MidPoint<grid.onedgrid.MidPoint>`;:math:`[-1,1]`;:math:`-1 + \frac{2i + 1}{N_{pts}}`;:math:`\frac{2}{n}`
:func:`Clenshow-Curtis<grid.onedgrid.ClenshawCurtis>`;:math:`[-1,1]`;:math:`\cos (\pi (i - 1) / (N_{pts} - 1))`;:math:`w_i = \frac{c_k}{n} \bigg(1 - \sum_{j=1}^{\lfloor n/2 \rfloor} \frac{b_j}{4j^2 - 1} \cos(2j\theta_i) \bigg), \quad b_j = 1 \text{ if } j = n/2, \quad 2 \text{ if } j < n/2, \quad c_j = 1 \text{ if } k \in \{0, n\}, \quad 2 \text{ else}`
:func:`Clenshaw-Curtis<grid.onedgrid.ClenshawCurtis>`;:math:`[-1,1]`;:math:`\cos (\pi (i - 1) / (N_{pts} - 1))`;:math:`w_i = \frac{c_k}{n} \bigg(1 - \sum_{j=1}^{\lfloor n/2 \rfloor} \frac{b_j}{4j^2 - 1} \cos(2j\theta_i) \bigg), \quad b_j = 1 \text{ if } j = n/2, \quad 2 \text{ if } j < n/2, \quad c_j = 1 \text{ if } k \in \{0, n\}, \quad 2 \text{ else}`
:func:`Fejer First<grid.onedgrid.FejerFirst>`;:math:`(-1,1)`;:math:`\cos\bigg(\frac{(2i - 1)\pi}{2N_{pts}}\bigg)`;:math:`\frac{2}{n}\bigg(1 - 2 \sum_{j=1}^{\lfloor n/2 \rfloor} \frac{\cos(2j \theta_j)}{4 j^2 - 1} \bigg)`
:func:`Fejer Second<grid.onedgrid.FejerSecond>`;:math:`(-1,1)`;:math:`\cos(i \pi / N_{pts})`;:math:`\frac{4 \sin(\theta_i)}{n} \sum_{j=1}^{\lfloor n/2 \rfloor} \frac{\sin(2j - 1)\theta_i}{2j - 1}`

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