Explicit and implicit methods: Difference between revisions

Revision as of 18:45, 27 December 2019

Revision as of 16:30, 28 December 2019

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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 analytical solution exists. Then one uses [[root-finding algorithm]]s, such as [[Newton's method]], to find the numerical solution.

;Crank NicolosonNicolson method:

With the [[Crank-Nicolson method]]

:<math>\frac{y_{k+1}-y_k}{\Delta t} = -\frac{1}{2}y_{k+1}^2 -\frac{1}{2}y_{k}^2</math>