# Implicit second order method

(Difference between revisions)
 Revision as of 00:55, 1 November 2005 (view source)Zxaar (Talk | contribs)← Older edit Latest revision as of 04:30, 15 February 2006 (view source)m (format) Line 1: Line 1: - = Implicit Second Order Method = + The '''implicit second order method''' involves the [[derivative]]s of the next time level. Due to this reason they are iterative in nature. The second order time integration scheme is given by: - + - 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:
+ ==Algorithm== ==Algorithm== Line 10: Line 8: :  end (r-loop)
:  end (r-loop)
- Where M is maximum number of internal iterations. + Here, ''M'' is maximum number of internal iterations. - + ---- ---- Return to [[Numerical methods | Numerical Methods]] Return to [[Numerical methods | Numerical Methods]]

## Latest revision as of 04:30, 15 February 2006

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:

## Algorithm

for r:= 1 step 1 until M do
$\phi ^{n + 1} = {4 \over 3}\phi ^n - {1 \over 3}\phi ^{n - 1} + {2 \over 3}\dot \phi \left( {t_{n + 1} ,\phi ^{n + 1} } \right) \bullet \Delta t$
end (r-loop)

Here, M is maximum number of internal iterations.