We propose and analyze methods for the numerical solution of anintegral equation which arises in statistical physics and spatialstatistics. Instances of this equation include the Mean Field,Poisson-Boltzmann and Emden equations for the density of a moleculargas, and the Poisson saddlepoint approximation for the intensity of aspatial point process. Conditions are established under which thePicard iteration and the under relaxation iteration converge.Numerical validation is included.
"Numerical solution of an integral equation from point process theory." J. Integral Equations Applications 26 (4) 437 - 452, WINTER 2014. https://doi.org/10.1216/JIE-2014-26-4-437