Backward Euler method: Difference between revisions

Revision as of 12:52, 24 March 2012

Revision as of 19:24, 28 March 2012

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Integrating the differential equation <math> y' = f(t,y) </math> from <math> t_k </math> to <math> t_{k+1} = t_k + h </math> yields

: <math> y(t_{k+1}) - y(t_k) = h \int_{t_k}^{t_{k+1}} f(\tau, y(\tau)) \,\mathrm{d}\tau. </math>

Now approximate the integral on the right by the right-hand [[rectangle method]] (with one rectangle):

: <math> y(t_{k+1}) - y(t_k) \approx h f(t_{k+1}, y(t_{k+1})) \,\mathrm{d}\tau. </math>