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Euler method

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Euler Methods

Explicit or Forward Euler

$\frac{d\phi}{dt} = f\left( {t,\phi } \right)$

$\phi ^{n + 1} = \phi ^n + f\left( {t_n ,\phi ^n } \right)$

Implicit or Backward Euler

$\frac{d\phi}{dt} = f\left( {t,\phi } \right)$

$\phi ^{n + 1} = \phi ^n + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right)$

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