Deriving Forward Euler and Backward/Implicit Euler Integration Schemes for Differential Equations
This video introduces and derives the simples numerical integration scheme for ordinary differential equations (ODEs): the Forward Euler and Backward Euler integration schemes. These integrators are based on the simplest forward and backward finite-different derivative approximations for dx/dt. Although these are not the best all-purpose integrators, they provide a great starting point for understanding sources of error and the stability of numerical integration techniques.
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This video was produced at the University of Washington
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0:00 Deriving Forward Euler Integration
14:24 Deriving Backward Euler Integration
19:03 Euler Integration for Linear Dynamics