Explicit and implicit methods: Difference between revisions

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Illustration using the forward and backward Euler methods: move comparison to what seems to be the desired ___location
Dr. TaO (talk | contribs)
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for <math>y_{k+1}</math>. This is a [[quadratic equation]], having one negative and one positive [[root (mathematics)|root]]. The positive root is picked because in the original equation the initial condition is positive, and then <math>y</math> at the next time step is given by
: <math>y_{k+1}=\frac{-1+\sqrt{1+4y_k4\Delta t y_k}}{2 \Delta t} \quad \quad (4)</math>.
 
In the vast majority of cases the equation to be solved for is much more complicated than a quadratic equation, and no exact solution exists. Then one uses [[root-finding algorithm]]s, such as [[Newton's method]].