Stability of Forward Euler and Backward Euler Integration Schemes for Differential Equations
In this video, we explore the stability of the Forward Euler and Backward/Implicit Euler integration schemes. In particular, we investigate the eigenvalues of these discrete-time update equations, relating the eigenvalues to the stability of the algorithm. This basic stability analysis technique, based on the eigenvalues of the update equation, applies to much more powerful integrators.
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This video was produced at the University of Washington
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0:00 Overview and goals of stability analysis
2:56 Stability of continuous dynamics
6:57 Stability of discrete time dynamics
9:17 Eigenvalues in the complex plane
14:34 Stability of Euler integration for scalar dynamics
26:42 Stability of Euler integration for matrix systems