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The Backward Euler scheme is not A-stable. Between FE, BE and CN, only the latter is A-stable. |
→Analysis: The fact that it "includes the whole left half of the complex plane" does not imply in A-stability. The backward Euler method may converge to an artificial solution when the dynamics of the real system is unstable (hence, not A-stable). |
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The backward Euler method has order one. This means that the [[local truncation error]] (defined as the error made in one step) is <math> O(h^2) </math>, using the [[big O notation]]. The error at a specific time <math> t </math> is <math> O(h) </math>.
The [[region of absolute stability]] for the backward Euler method is the complement in the complex plane of the disk with radius 1 centered at 1, depicted in the figure.<ref>{{harvnb|Butcher|2003|p=70}}</ref> This includes the whole left half of the complex plane
== Extensions and modifications ==
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