Function f(t) specified on [t_0;t_1] has a necessary number of derivatives. Find algorithm which can build uniform approximations of this function with help of partial sums:
\sum_{i=1}^{N}\alpha_i e^{-\beta_i t}.
That is, find such \alpha_i, Re(\beta_i)\geq 0 satisfying the expression...
We must find the resistance between opposite vertices, not adjacent. The second problem is too easy rather than the first :)
Here is the picture of the problem discussed:
http://rghost.ru/3908/download/22312f648e26dabce002e347898f5242c521aa58/Hexagons.pdf" [Broken]
This is a misunderstanding. :) I have already solved this problem. I was only trying to represent it to the people, who are interested in it. But I suppose I wrote this problem in the wrong forum section... Dick, please, if you have the answer, write me a private message. We'll check the result ;)
We have an infinite net of regular hexagons. Each side of hexagons has a resistance R. What is the resistance between two opposite vertexes of hexagon(s)?
Sorry for my English. :)
Let function f(x) defined on [a,b] and its table f(x_k) determined in equidistant interpolation nodes x_k k=0,1,..,n with step h=\frac{b-a}{n}.
Inaccuracy of piecewise-polynomial interpolation of power s (with the help of interpolation polynoms P_s(x,f_{kj}) on the x_k...
But actually, I didn't use differential equation :)
\frac{1}{a_{n+1}}=\frac{1+\left|sin(a_n)\right|}{a_n}
It's easy to show that a_n is going to zero at large n, but remains postive. So:
\frac{1}{a_{n+1}}=\frac{1+a_n-\frac{1}{6}a_n^3+o(a_n^3)}{a_n} =\frac{1}{a_n}+1+b_n, where b_n \rightarrow...