This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.
Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a surprisingly common phenomenon. Many standard numerical methods applied to stiff systems of ODE's will either yield an unstable iteration that grows without limit, or just grind to a halt. Stiffness is frequently a mathematical manifestation of a physical problem that has two or more very different scales for the independent variable. There are numerical ODE methods well-suited to handling stiff systems and we illustrate these methods with examples. The material is suitable for an introductory ODE course in which students have encountered systems of ODE's (at least, linear systems) and basic numerical methods, for example, Euler's method.
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