Backward Euler method: Difference between revisions

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The [[Stiff_equation#Runge%E2%80%93Kutta_methods|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, making it suitable for the solution of [[stiff equation]]s.<ref>{{harvnb|Butcher|2003|p=71}}</ref> In fact, the backward Euler method is even [[L-stability|L-stable]].

The region for a discrete '''stable''' system by Backward Euler Method is a circle with radius 0.5 which is located at (0.5, 0) in the z-plane.<ref>[http://b-ok.xyz/book/600092/2d1ce9], Wai-Kai Chen, Ed., Analog and VLSI Circuits The Circuits and Filters Handbook, 3rd ed. Chicago, USA: CRC Press, 2009.</ref>.

== Extensions and modifications ==