# Euler method

### From CFD-Wiki

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=== Explicit or Forward Euler === | === Explicit or Forward Euler === | ||

- | :<math> \ | + | :<math> \frac{d\phi}{dt} = f\left( {t,\phi } \right)</math> |

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:<math>\phi ^{n + 1} = \phi ^n + f\left( {t_n ,\phi ^n } \right) </math> | :<math>\phi ^{n + 1} = \phi ^n + f\left( {t_n ,\phi ^n } \right) </math> | ||

=== Implicit or Backward Euler === | === Implicit or Backward Euler === | ||

- | :<math> \ | + | :<math> \frac{d\phi}{dt} = f\left( {t,\phi } \right)</math> |

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:<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> | ||

## Latest revision as of 17:44, 14 December 2005

## Euler Methods

### Explicit or Forward Euler

### Implicit or Backward Euler

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