# Euler method

(Difference between revisions)
 Revision as of 04:13, 14 November 2005 (view source)Zxaar (Talk | contribs)← Older edit Latest revision as of 17:44, 14 December 2005 (view source)Tsaad (Talk | contribs) (Changed phi_dot to dPhi/dt) (2 intermediate revisions not shown) Line 2: Line 2: === Explicit or Forward Euler === === Explicit or Forward Euler === - :$\dot \phi = f\left( {t,\phi } \right)$ + :$\frac{d\phi}{dt} = f\left( {t,\phi } \right)$ + + :$\phi ^{n + 1} = \phi ^n + f\left( {t_n ,\phi ^n } \right)$ :$\phi ^{n + 1} = \phi ^n + f\left( {t_n ,\phi ^n } \right)$ === Implicit or Backward Euler === === Implicit or Backward Euler === - :$\dot \phi = f\left( {t,\phi } \right)$ + :$\frac{d\phi}{dt} = f\left( {t,\phi } \right)$ + + :$\phi ^{n + 1} = \phi ^n + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right)$ :$\phi ^{n + 1} = \phi ^n + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right)$ + + {{stub}} + ---- + Return to [[Numerical methods | Numerical Methods]]

## 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

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

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