Explicit and implicit methods: Difference between revisions

Revision as of 23:03, 4 January 2017

Revision as of 23:04, 4 January 2017

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:<math>Y(t+\Delta t) = F(Y(t+\Delta t))+G(Y(t)),\,</math>

while one is treated explicitly and the other implicitly

For usual applications the implicit term is chosen to be linear while the explicit term can be nonlinear. This combination of the former method is called '''Implicit-Explicit Method''' (short IMEX <ref>U.M. Ascher, S.J. Ruuth, R.J. Spiteri: ''Implicit-Explicit Runge-Kutta Methods

for Time-Dependent Partial Differential Equations'', Appl Numer Math, vol. 25(2-3), 1997</ref>).