APPROXIMATION TO INTEGRALS WITH VARYING LIMITS AND ITS APPLICATION TO CALCULATE THE THIRD-ORDER DEBYE FUNCTIONS
V. G. Eliseyev, G. M. Eliseyev
VANT. Ser.: Mat. Mod. Fiz. Proc 2006. Вып.3. С. 59-65.
The paper offers the approximation algorithm for functions, which are a product of the two multiplier factors: an integral with varying limits and another, more simple function. The case with one varying limit (the upper limit) is considered for the sake of simplicity. It is easy to built approximation to the integral factor only. Then, one can calculate the original function derivatives to the same accuracy using the product differentiation formulas. To build the required approximation, we suggest using local Hermitian interpolation, on average, polynomial splines of the fourth order, which are constructed basing on the reference tables of histogram and the first two derivatives of the integral factor. Maple software was used to obtain all the required formulas for the given spline construction. A five-place spline approximation to the third-order Debye function has been constructed for an example. Fortran program texts for calculation of the Debye function values are presented.
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