Torsten Mayer-Gurr,来自德国波恩大学的一名学者，感谢他的这份邮件，解决了我的一个大疑惑。在此，我真体会到了国外学者的友好、严谨、乐于助人的品格了。估计在国内，没有哪个牛人会搭理我们这种无名小辈的，而在国外，则截然相反，这是为什么呢？

Dear You Wei,
Thank you for your interest in our paper.
First of all some general remarks about the idea of our method:
Our method to compute nummerically the integral (B2) is the following:
first of all the integral (B2) is divided into pieces of 30 seconds
length (intervall between two observations) and each intervall is
integrated seperatly. The function f is approximated by an interpolation
polynomial. For the integral in each intervall a closed expression can
be found if only polynomials in it.
We described here a very complicated way to compute this polynomials (By
series of legendre polynomial and Gauss-Legendre quadrature). After this
paper was puplished I found a much simpler way to compute this integral.
The method is written in Phd thesis but it is only in german available,
unfortunately. I send you the thesis anyway because the interesting part
contains little text but a lot of equations.
The interesting part starts at eq.(4.64), page 46. The integral is
divided into 30s intervalls (sum over k). In the next step the
boundaries are normalized to (0,1) by changing the intergation variable
from tau’ to t, Eq. (4.66). The force function f is now approximated by
an interpolation polynomial, Eq. (4.68), (see also fig. 4.2, the blue
area is the integration intervall). The coefficients a_nk oth the
polynomial can be computed by Eq. (4.70) where w_nj the coefficients of
the inverse of the matrix in Eq. (4.16). This matrix is constant and
must be computed only once. In Eq. (4.71) is the result of the
nummerical integration.
I think you should use this and not the method described in the paper.
If want to understand the method used in the paper you should ask by my
co-author Karl-Heinz Ilk. The appendix was written by him.
best regards
Torsten