Explicit and implicit methods: Difference between revisions

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;Forward Euler method:
The forward Euler method
:<math>\left(\frac{dy}{dt}\right)_k = \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>