https://cfd-online.com/W/index.php?title=Implicit_second_order_method&feed=atom&action=historyImplicit second order method - Revision history2024-03-28T13:32:32ZRevision history for this page on the wikiMediaWiki 1.16.5https://cfd-online.com/W/index.php?title=Implicit_second_order_method&diff=5288&oldid=prevOleg Alexandrov: format2006-02-15T04:30:31Z<p>format</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 04:30, 15 February 2006</td>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">= Implicit Second Order Method =</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The <ins class="diffchange diffchange-inline">'''</ins>implicit second order method<ins class="diffchange diffchange-inline">''' </ins>involves the <ins class="diffchange diffchange-inline">[[derivative]]s </ins>of the next time level. Due to this reason they are iterative in nature. The second order time integration scheme is given by: </div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The implicit second order method involves the <del class="diffchange diffchange-inline">derivatives </del>of the next time level. Due to this reason they are iterative in nature. The second order time integration scheme is given by: <del class="diffchange diffchange-inline"><br></del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Algorithm==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Algorithm==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: end (r-loop) <br> </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>: end (r-loop) <br> </div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline"><i> Where </del>M is maximum number of internal iterations. <del class="diffchange diffchange-inline"></i></del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Here, ''</ins>M<ins class="diffchange diffchange-inline">'' </ins>is maximum number of internal iterations.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>----</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>----</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><i> Return to [[Numerical methods | Numerical Methods]] </i></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><i> Return to [[Numerical methods | Numerical Methods]] </i></div></td></tr>
</table>Oleg Alexandrovhttps://cfd-online.com/W/index.php?title=Implicit_second_order_method&diff=3473&oldid=prevZxaar at 00:55, 1 November 20052005-11-01T00:55:55Z<p></p>
<p><b>New page</b></p><div>= Implicit Second Order Method =<br />
<br />
The implicit second order method involves the derivatives of the next time level. Due to this reason they are iterative in nature. The second order time integration scheme is given by: <br><br />
<br />
==Algorithm==<br />
<br />
: for r:= 1 step 1 until M do <br><br />
::<math>\phi ^{n + 1} = {4 \over 3}\phi ^n - {1 \over 3}\phi ^{n - 1} + {2 \over 3}\dot \phi \left( {t_{n + 1} ,\phi ^{n + 1} } \right) \bullet \Delta t<br />
</math><br />
: end (r-loop) <br> <br />
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<i> Where M is maximum number of internal iterations. </i><br />
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<br />
----<br />
<i> Return to [[Numerical methods | Numerical Methods]] </i></div>Zxaar