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Euler method

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:<math> \dot \phi  = f\left( {t,\phi } \right)</math>
:<math> \dot \phi  = f\left( {t,\phi } \right)</math>
:<math>\phi ^{n + 1}  = \phi ^n  + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right) </math>
:<math>\phi ^{n + 1}  = \phi ^n  + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right) </math>
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<i> Return to [[Numerical methods | Numerical Methods]] </i>

Revision as of 04:13, 14 November 2005

Euler Methods

Explicit or Forward Euler

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

Implicit or Backward Euler

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



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