Explicit and implicit methods: Difference between revisions

Revision as of 05:31, 3 May 2016

Revision as of 19:34, 19 July 2016

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[[File:Forward and backward Euler method.png|thumb|350px|The result of applying the two methods with <math>a = 5</math> and <math>n = 30</math>.]]

The forward [[Euler method]]

:<math>\left(\frac{dy}{dt}\right)_k =\approx \frac{y_{k+1}-y_k}{\Delta t} = - y_k^2</math>

yields

: <math>y_{k+1}=y_k-\Delta t y_k^2 \quad \quad \quad(3)\, </math>