Explicit and implicit methods: Difference between revisions

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Since the implicit method cannot be carried out for each kind of differential operator, it is sometimes advisable to make use of the so called operator splitting method, which means that the differential operator is rewritten as the sum of two complimental operators

:<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>).