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The backward Euler method is an implicit method: the new approximation <math> y_{k+1} </math> appears on both sides of the equation, and thus the method needs to solve an algebraic equation. Sometimes, this can be done by [[fixed-point iteration]]:
:<math> y_{k+1}^{[0]} = y_k, \quad y_{k+1}^{[i+1]} = y_k + h f(t_{k+1
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>
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