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Implicit second order method

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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:


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.

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