摘要:

We show that the dual of a collocation method, for solving a Fredholm integral equation of the second kind, is a particle method, that is a method where the data is approximated by weighted Dirac measures.

ISSN:0041-1450    

DOI:10.1080/00411458608212705

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

A solution of the one dimensional Vlasov equation is compared to the motion of a system of particles interacting through the one dimensional Coulomb potential. For each value of the time t, both the distribution function f(t) and the system of point particles II (t) are considered as elements of the dual space of a suitable vector space of test functions. It is shown that for a fixed solution f(t) of the Vlasov equation, if II (0) tends to f(o) in the chosen dual space, then n(t) tends to f(t) for all t > 0.

ISSN:0041-1450    

DOI:10.1080/00411458608212706

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

The Spencer-Lewis equation, which describes electron transport in homogeneous media when continuous slowing down theory is valid, is derived from the Boltzmann equation. Also derived is a time-dependent generalized Spencer-Lewis equation valid for inhomogeneous media. An independent verification of this last equation is obtained for the one-dimensional case using particle balance considerations.

ISSN:0041-1450    

DOI:10.1080/00411458608212707

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

Spectral and pseudospectral methodr for spatially discretiring the first-order transport equation in slab geometry are discussed and compared with finite element and other discretization methods. Spectral methods are shown to have exponential (“infinite order”) convergence for homogeneous problems, enabling them to achieve extremely accurate solutions at lower computational costs than other methods. A “spectral element” method is proposed which extends this exponential convergence to heterogeneous problems. Numerical results are given supporting all theoretical claims, and applicability of the method to physically significant problems is discussed. We conclude that the spectral element method is probably useful mainly for high-accuracy calculations of one-dimensional problems; in higher dimensions the transport solution lacks the smoothness which for realistic problems would allow the method to achieve exponential convergence.

ISSN:0041-1450    

DOI:10.1080/00411458608212708

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

This paper studies the existence problem for the weak Enskog equation in two space-variables far from equilibrium. As a corollary we get a new existence result for the spatially homogeneous Boltzmann equation for inverse vth power forces and angular cut-off when 2 <v⩽ 3.

ISSN:0041-1450    

DOI:10.1080/00411458608212709

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

摘要:

E. E. Lewis and W. F. Miller, Jr., John Wiley and Sons, NY, 1985. 396 pp. $44.95.

ISSN:0041-1450    

DOI:10.1080/00411458608212710

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411458608212711

出版商:Taylor & Francis Group    

年代:1986

数据来源: Taylor