3.7Improvements to Euler Integration
Euler integration is popular in large measure due to its simplicity. A graphical interpretation of either explicit or implicit Euler integration is straightforward. A discussion of error characteristics for Euler integrators is deferred until a later chapter. However, its apparent that serious errors can propagate as the discrete-time variable “n” increases with Euler integration as a result of the underlying assumption that the state derivative remains constant for an entire integration step. For systems in which one or more of the state variables experience frequent fluctuations (relative to the integration step size) this assumption is unjustified.
The inherent weakness of Euler integration can be overcome ...
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