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Summation equation

About: Summation equation is a(n) research topic. Over the lifetime, 4041 publication(s) have been published within this topic receiving 77010 citation(s). The topic is also known as: discrete integral equation.
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Journal ArticleDOI
01 Jan 1962-Journal of the ACM
TL;DR: Here the authors will consider only nonsingular linear integral equations of the first kind, where the known functions h(x), K(x, y) and g(x) are assumed to be bounded and usually to be continuous.
Abstract: where the known functions h(x) , K(x, y) and g(x) are assumed to be bounded and usually to be continuous. If h(x) ~0 the equation is of first kind; if h(x) ~ 0 for a -<_ x ~ b, the equation is of second kind; if h(x) vanishes somewhere but not identically, the equation is of third kind. If the range of integration is infinite or if the kernel K(x, y) is not bounded, the equation is singular. Here we will consider only nonsingular linear integral equations of the first kind:

1,814 citations


Book
01 Jan 1992-

1,508 citations


Journal ArticleDOI
Abstract: ABS>The equation of state and the pair distribution for the Percus- Yevick integral equation for the radiai distribution function of a classical fluid are obtained in closed form for the prototype of interacting hard spheres. (D.C.W.)

1,373 citations


Book ChapterDOI
Hannes Risken1
01 Jan 1984-
Abstract: As shown in Sects 31, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (31, 31) For nonlinear Langevin equations (367, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function As mentioned already in the introduction, a differential equation for the distribution function describing Brownian motion was first derived by Fokker [11] and Planck [12]: many review articles and books on the Fokker-Planck equation now exist [15 – 15]

1,296 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20212
20203
20195
20184
201773
2016100

Top Attributes

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Topic's top 5 most impactful authors

Khosrow Maleknejad

11 papers, 468 citations

Stevo Stević

8 papers, 110 citations

Robert E. Kalaba

6 papers, 36 citations

Rainer Kress

5 papers, 122 citations

Luigi Verolino

4 papers, 20 citations