Can I Scale Down Basis Functions Without Losing Zero Force?

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SUMMARY

The discussion centers on scaling down basis functions ##\phi_i(x)## that exhibit rapid growth, specifically around ##O(\sinh(12 j))## for the ##jth## function. The user successfully forced these functions to approach zero at specific points (3 and 3.27), but the values remain significantly large, with instances like ##\phi(x=3) = 10^{16}## compared to an average height of ##10^{30}##. The user seeks methods to effectively reduce the magnitude of these functions without losing the zero force condition.

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Hi PF!

I'm working with some basis functions ##\phi_i(x)##, and they get out of control big, approximately ##O(\sinh(12 j))## for the ##jth## function. What I am doing is forcing the functions to zero at approximately 3 and 3.27. I've attached a graph so you can see. Looks good, but in fact these values are very far from zero. Any ideas on what I can do to get these scaled down significantly so they are forced to zero?

I should say, each function individually get very close to zero regarding it's size, but for some cases that means ##\phi(x=3) = 10^{16}##, which is very small considering it's average height is about ##10^{30}## with sharp gradients.
 

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Nevermind, I have it working now!
 

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