Explicit and implicit methods: Difference between revisions

Revision as of 18:29, 2 July 2021

Revision as of 18:29, 2 July 2021

Line 21:

;Forward Euler method:

[[File:Result of applying integration schemes.png|thumb|The result of applying different integration methods to odethe ODE: <math> y'=-y^2, \; t\in[0, 5], \; y_0=1 </math> with <math>\Delta t = 5/10</math>.]]

The forward [[Euler method]]

:<math>\left(\frac{dy}{dt}\right)_k \approx \frac{y_{k+1}-y_k}{\Delta t} = - y_k^2</math>