Solving equations with fractional exponents Newton's Method -Non-linear systems ```Name: Unknown Status: N/A Age: N/A Location: N/A Country: N/A Date: Around 1993 ``` Question: Replies: This is hard, but I will try to explain as much as I can in the simplest manner possible. This is a "new" area and was a great surprise when it became clear. Linear systems are systems in which the forces are either constants or are linear functions of space variables. A spring and a mass (ideal spring) are exactly a linear system. The motion for such a system is very simple and represents simple oscillatory motion (often easily represented by sines and cosines of time). Non-linear systems have forces that are not linear functions of the space variables and the surprise is that the non- linear systems have very little long time predictability. In other words, two such systems that started out with very close to the same initial conditions (position, velocity) can end up after a long enough time very far apart. This means that we cannot make accurate predictions over long times. The weather is an excellent example. It appears that we cannot get accurate predictions from our computer models for longer than about 10 to 14 days. Running them over this time will not be dependable. It is not a problem of inadequate starting data, but has to do with the nature of the forces between air masses. Let me know if this was an understandable answer. Samuel B. Bowen Click here to return to the Mathematics Archives

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