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Apr
14
comment Differential Equation with Numerically Integrated Boundary Conditions
I have edited the original question to clear up the confusion you mention in your answer. In short, the curve's lengths/end-points shouldn't change, since in my case I'm modeling an inextensible elastica.
Apr
14
revised Differential Equation with Numerically Integrated Boundary Conditions
clarify question
Apr
14
comment Differential Equation with Numerically Integrated Boundary Conditions
Thanks @J.M., I really like this framework. I am familiar with this equation as Euler's elastica, and I'm aware of its analytical solution by way of elliptic integrals. Part of the focus behind this question is to have a numerical toolset to go along with the analytical one.
Apr
13
revised Differential Equation with Numerically Integrated Boundary Conditions
closer to solutution
Apr
13
awarded  Commentator
Apr
13
revised Differential Equation with Numerically Integrated Boundary Conditions
improved formatting, clarified question, attempted solution
Apr
13
revised Differential Equation with Numerically Integrated Boundary Conditions
fixed incorrect link
Apr
13
comment Differential Equation with Numerically Integrated Boundary Conditions
I don't have working code with those boundary conditions. I would like to study this equation as I vary \[Kappa][1] (which, in the code above is \[Kappa][1] == 1). If you run the code for different values of \[Kappa][1], you'll see that x[1] varies, though I'd like it to remain fixed at x[1]==0.
Apr
13
asked Differential Equation with Numerically Integrated Boundary Conditions
Mar
29
awarded  Benefactor
Mar
29
accepted How can I optimize the search between two lists, one that is changing length?
Mar
23
comment How can I optimize the search between two lists, one that is changing length?
using your code improvements I was able to run the n=5 case (the timing was {1630.49, Null}. One question I have is in regards to how Association adds the data to the list. I'm trying to export the final value as a CSV file where each 5 x 5 array that is stored in uniqueArray is separated by a comma, but I'm getting some strange delimiters between the arrays, e.g. the first characters are <|, and in between each array is ->1 The code I'm using to export is: Export["uniqueArray.txt", uniqueArray, "CSV", "TextDelimiters" -> None]
Mar
23
comment How can I optimize the search between two lists, one that is changing length?
Ahh, ok, that's my fault - I added those lines of m[1]; // AbsoluteTiming to the question to quickly show the timing, but those lines are not in the code I run. I should clarify that.
Mar
22
comment How can I optimize the search between two lists, one that is changing length?
Excellent, that's a really helpful and significant speed up. Is there any reason I don't see any of these warnings? My messages are blank.
Mar
22
comment How can I optimize the search between two lists, one that is changing length?
Thanks nikie - I recognize that getting much past n=6 is essentially impossible. Perhaps there's a better algorithm, yet I haven't been able to think about one. Get the results for n=5 and n=6 would be a victory. Is there a syntax change needed to switch AppendTo with Association? When I substituted the latter it didn't write anything to the nested list.
Mar
22
awarded  Promoter
Mar
22
revised How can I optimize the search between two lists, one that is changing length?
added 1350 characters in body
Mar
18
awarded  Tumbleweed
Mar
11
asked How can I optimize the search between two lists, one that is changing length?
Mar
3
awarded  Supporter