Explicit and implicit methods: Difference between revisions

Revision as of 08:35, 14 August 2009

Revision as of 15:45, 11 November 2009

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for <math>y_{k+1}</math> (compare this with formula (3) where <math>y_{k+1}</math> was given explicitly rather than as an unknown in an equation).

This is a [[quadratic equation]], having one negative and one positive [[rootRoot (mathematics)of a function|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+4\Delta t y_k}}{2 \Delta t}. \quad \quad (4)</math>