Euler method

(Difference between revisions)

Latest revision as of 17:44, 14 December 2005

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

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

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

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

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 === Explicit or Forward Euler ===
-:<math> \dot \phi  = f\left( {t,\phi } \right)</math>
+:<math> \frac{d\phi}{dt}  = f\left( {t,\phi } \right)</math>
 :<math>\phi ^{n + 1}  = \phi ^n  + f\left( {t_n ,\phi ^n } \right) </math>
 === Implicit or Backward Euler ===
-:<math> \dot \phi  = f\left( {t,\phi } \right)</math>
+:<math> \frac{d\phi}{dt}  = f\left( {t,\phi } \right)</math>
 :<math>\phi ^{n + 1}  = \phi ^n  + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right) </math>