Spectral Methods in Chemistry and Physics by Bernard Shizgal

Spectral Methods in Chemistry and Physics by Bernard Shizgal

Author:Bernard Shizgal
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht


(4.38)

where

(4.39)

The recurrence relation has been used twice as well as the integral identity in Eq. (4.16). This result should be compared with approximation of the temperature, Eq. (4.28), with the asymmetric expansion, Eq. (4.13).

Fig. 4.2Demonstration of spectral (that is exponential) convergence of the expansion of a Maxwellian at in Hermite polynomials, , with defined at with and is a scale factor. The left hand frame shows the spectral convergence for and different values of (from top to bottom) whereas the right hand frame is for and different values of (from top to bottom). The symbols are the numerical results from Eq. (4.37) and the straight lines are linear least squares fits to the symbols. In Table 4.2, the slopes of the lines are compared with the asymptotic results of Eq. (4.37)



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