Explicit and implicit methods: Difference between revisions

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Illustration using the forward and backward Euler methods: an exact solution does exist in most cases, there is just no formula (analytical solution) for it
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: <math>y_{k+1}=\frac{-1+\sqrt{1+4\Delta t y_k}}{2 \Delta t}. \quad \quad (4)</math>
 
In the vast majority of cases, the equation to be solved when using an implicit scheme is much more complicated than a quadratic equation, and no exactanalytical solution exists. Then one uses [[root-finding algorithm]]s, such as [[Newton's method]], to find the numerical solution.
 
==See also==