Explicit and implicit methods: Difference between revisions

Revision as of 07:55, 11 March 2022

Revision as of 04:16, 28 December 2024

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one finds the implicit equation

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

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 can be numerically solved using [[root-finding algorithm]]s, such as [[Newton's method]], to obtain <math>y_{k+1}</math>.