Explicit and implicit methods: Difference between revisions

Revision as of 02:00, 10 January 2006

Revision as of 06:58, 9 March 2006

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to find <math>Y(t+\Delta t).</math>

It is immediate thenclear that implicit methods require an extra computation (solving the above equation), and can also be much harder to implement. The reason one uses implicit methods is that for great many problems (called [[stiff problem]]s) using an explicit method requires extremely small time steps <math>\Delta t</math> for the error of the method to not explode to infinity (see [[numerical stability]]),. and then it isIt takes much less computational time to use an implicit method with larger time steps, even taking into account that one needs to solve an equation of the form (1) at each time step. As such, the choice between which method to use depends on the specific problem at hand.

==Illustration using the forward and backward Euler methods==