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The AD method for the approximate solution of the Wigner equations

The AD method for the approximate solution of the Wigner equations DEMONSTRATIO MATHEMATICAVol. XXVIINo 21994P h a n Van Hap, Phan H u y ThienT H E A D M E T H O D FOR T H E A P P R O X I M A T E S O L U T I O NOF T H E W I G N E R E Q U A T I O N SIn [1], [2] was given the definition of the (integral) average derivate and itsapplication to the approximate solution of the generalized diffusion problemand some boundary problems.The method is based on the average differentiation and will be calledthe AD method. This paper presents the AD method for the approximatesolution of the Wigner equations.1.haveDEFINITION,a) Let F : Q + r -> ft + r c X-Banach space; if welim^)"1 f-sn X o + th}-F{Xo)dt=dF(x0,h)for all h, xq, xo + h € Q + r, then this limit is called the first averagevariation of F at x0.b) If at xo we have dF(x o; h) = Ah, where A is abounded linear operator,then F is called the average differentiation and F(xo; h) = Ah = dF(xo; h)is the average derivative of F at xo.Remarks:a) There exist the function http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

The AD method for the approximate solution of the Wigner equations

Hap, Phan Van; Thien, Phan Huy
Demonstratio Mathematica , Volume 27 (2): 4 – Apr 1, 1994
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Publisher
de Gruyter
Copyright
© by Phan Van Hap
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1994-0205
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XXVIINo 21994P h a n Van Hap, Phan H u y ThienT H E A D M E T H O D FOR T H E A P P R O X I M A T E S O L U T I O NOF T H E W I G N E R E Q U A T I O N SIn [1], [2] was given the definition of the (integral) average derivate and itsapplication to the approximate solution of the generalized diffusion problemand some boundary problems.The method is based on the average differentiation and will be calledthe AD method. This paper presents the AD method for the approximatesolution of the Wigner equations.1.haveDEFINITION,a) Let F : Q + r -> ft + r c X-Banach space; if welim^)"1 f-sn X o + th}-F{Xo)dt=dF(x0,h)for all h, xq, xo + h € Q + r, then this limit is called the first averagevariation of F at x0.b) If at xo we have dF(x o; h) = Ah, where A is abounded linear operator,then F is called the average differentiation and F(xo; h) = Ah = dF(xo; h)is the average derivative of F at xo.Remarks:a) There exist the function

Journal

Demonstratio Mathematica – de Gruyter

Published: Apr 1, 1994

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