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Time‐Varying Weight Functions and the Convergence of Polynomial Expansions

 

作者: Lowell H. Holway,  

 

期刊: Physics of Fluids(00319171)  (AIP Available online 1967)
卷期: Volume 10, issue 1  

页码: 35-48

 

ISSN:0031-9171

 

年代: 1967

 

DOI:10.1063/1.1761992

 

出版商: AIP

 

数据来源: AIP

 

摘要:

Expansions are given for isotropic distribution functions in a series of polynomials orthogonal with respect to a time‐dependent Maxwellian weight function. It is shown that the choice of the weight function can affect the rate of convergence or, indeed, whether the expansion will converge at all. For the case of the Fokker‐Planck equation describing the relaxation of electrons in a Lorentz gas, the infinite matrix determining the time dependence of the expansion coefficients is diagonalized by an appropriate choice of the weight function. The equilibrium expansion of Kahalas and Kashian and Osipov's result for an initial Maxwellian are special cases of our more general formulation. An alternative expansion method is discussed which can be expected to converge for all realistic distribution functions. Applications to the theory of plane shock waves are suggested.

 

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