Mathematica Can I Scale Down Basis Functions Without Losing Zero Force?

AI Thread Summary
The discussion focuses on the challenge of scaling down basis functions that grow excessively large, specifically around the values of 3 and 3.27, while maintaining their zero force condition. The functions exhibit a growth rate of approximately O(sinh(12j), leading to extreme values like φ(x=3) = 10^16 against an average height of 10^30. The user initially sought advice on how to significantly reduce these values while ensuring they approach zero. Ultimately, the user reports that they have found a solution to the problem. The conversation highlights the complexities of managing basis function behavior in mathematical modeling.
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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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