Content deleted Content added
Clean Copy (talk | contribs) →Illustration using the forward and backward Euler methods: move comparison to what seems to be the desired ___location |
|||
Line 29:
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+
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]].
|