Backward Euler method: Difference between revisions

Revision as of 11:17, 25 March 2016

Revision as of 07:11, 26 March 2016

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:<math> y_{k+1}^{[0]} = y_k, \quad y_{k+1}^{[i+1]} = y_k + h f(t_{k+1}, y_{k+1}^{[i]}). </math>

If this sequence converges (within a given tolerance), then the method takes its limit as the new approximation

<math> y_{k+1} </math>. <ref>{{harvnb|Butcher|2003|p=57}}</ref>

Alternatively, one can use (some modification of) the [[Newton's method|Newton–Raphson method]] to solve the algebraic equation.

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[[Category:Numerical differential equations]]

[[Category:Runge–Kutta methods]]

: <math> \int__{t_n}^{t_{n+1}} \,