Volume 26, pp. 385-420, 2007.

Stability properties of differential-algebraic equations and spin-stabilized discretizations

Peter Kunkel and Volker Mehrmann

Images and movies related to the paper

The following table contains links to images and movies of the stability regions for various discretization methods applied to the proposed test function.

Method Image Movie
Implicit Euler method X X
Radau IIa method s=2 X X
Radau IIa method s=3 X  
Implicit midpoint rule X X
Gauss method s=2 X  
Gauss-Lobatto method k=1 X X
Gauss-Lobatto method k=2 X  
Trapezoidal rule X  
BDF method k=2 X X

The stability regions for Example 1 of the un-stabilized implicit Euler method can be found here and of the spin-stabilized implicit Euler method can be found here.