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Stability of Forward Euler and Backward Euler Integration Schemes for Differential Equations 1 год назад


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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. Playlist:    • Engineering Math: Differential Equati...   Course Website: http://faculty.washington.edu/sbrunto... @eigensteve on Twitter eigensteve.com databookuw.com This video was produced at the University of Washington %%% CHAPTERS %%% 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

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