CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Wiki > Euler method

Euler method

From CFD-Wiki

(Difference between revisions)
Jump to: navigation, search
(Changed phi_dot to dPhi/dt)
 
(2 intermediate revisions not shown)
Line 2: Line 2:
=== Explicit or Forward Euler ===
=== 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>
:<math>\phi ^{n + 1}  = \phi ^n  + f\left( {t_n ,\phi ^n } \right) </math>
=== Implicit or Backward Euler ===
=== 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>
:<math>\phi ^{n + 1}  = \phi ^n  + f\left( {t_{n + 1} ,\phi ^{n + 1} } \right) </math>
 +
 +
{{stub}}
 +
----
 +
<i> Return to [[Numerical methods | Numerical Methods]] </i>

Latest revision as of 17:44, 14 December 2005

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)



Return to Numerical Methods

My wiki