Numerical solution of an integral equation from point process theory

R.S. Anderssen; Adrian Baddeley; F.R. De Hoog; Gopalan Nair

doi:10.1216/JIE-2014-26-4-437

Numerical solution of an integral equation from point process theory

R.S. Anderssen, Adrian Baddeley, F.R. De Hoog, Gopalan Nair

Research output: Contribution to journal › Article › peer-review

3 Citations (Web of Science)

Abstract

© 2014 Rocky Mountain Mathematics Consortium. We propose and analyze methods for the numerical solution of an integral equation which arises in statistical physics and spatial statistics. Instances of this equation include the Mean Field, Poisson-Boltzmann and Emden equations for the density of a molecular gas, and the Poisson saddlepoint approximation for the intensity of a spatial point process. Conditions are established under which the Picard iteration and the under relaxation iteration converge. Numerical validation is included.

Original language	English
Pages (from-to)	437-453
Journal	Journal of Integral Equations and Applications
Volume	26
Issue number	4
DOIs	https://doi.org/10.1216/JIE-2014-26-4-437
Publication status	Published - 2014

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abstract = "{\textcopyright} 2014 Rocky Mountain Mathematics Consortium. We propose and analyze methods for the numerical solution of an integral equation which arises in statistical physics and spatial statistics. Instances of this equation include the Mean Field, Poisson-Boltzmann and Emden equations for the density of a molecular gas, and the Poisson saddlepoint approximation for the intensity of a spatial point process. Conditions are established under which the Picard iteration and the under relaxation iteration converge. Numerical validation is included.",

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AU - Anderssen, R.S.

AU - Baddeley, Adrian

AU - De Hoog, F.R.

AU - Nair, Gopalan

PY - 2014

Y1 - 2014

N2 - © 2014 Rocky Mountain Mathematics Consortium. We propose and analyze methods for the numerical solution of an integral equation which arises in statistical physics and spatial statistics. Instances of this equation include the Mean Field, Poisson-Boltzmann and Emden equations for the density of a molecular gas, and the Poisson saddlepoint approximation for the intensity of a spatial point process. Conditions are established under which the Picard iteration and the under relaxation iteration converge. Numerical validation is included.

AB - © 2014 Rocky Mountain Mathematics Consortium. We propose and analyze methods for the numerical solution of an integral equation which arises in statistical physics and spatial statistics. Instances of this equation include the Mean Field, Poisson-Boltzmann and Emden equations for the density of a molecular gas, and the Poisson saddlepoint approximation for the intensity of a spatial point process. Conditions are established under which the Picard iteration and the under relaxation iteration converge. Numerical validation is included.

U2 - 10.1216/JIE-2014-26-4-437

DO - 10.1216/JIE-2014-26-4-437

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VL - 26

SP - 437

EP - 453

JO - Journal of Integral Equations and Applications

JF - Journal of Integral Equations and Applications

IS - 4

ER -

Numerical solution of an integral equation from point process theory

Abstract

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